Q:

How do interpretations of Hit Points vary among D&D editions?

Is it true that Hit Points in different editions mean different things in the game world?
For instance, hit points are quite abstract concept in 5e:

Hit points represent a combination of physical and mental durability, the will to live, and luck. Creatures with more hit points are more difficult to kill.

As a comparison, they represent two specific (but still quite broad) things in Pathfinder:

Hit points mean two things in the game world: the ability to take physical punishment and keep going, and the ability to turn a serious blow into a less serious one.

(I know PF is not exactly D&D, but the idea should be similar to the D&D 3.5 edition, I guess)
I'm not familiar with the prior editions. What did HP mean earlier?

A:

Hit Points (HP): how they are treated, comparison across editions
TL:DR - as it was in the beginning1, hit points are mostly an abstraction that indicate whether the character/creature is alive or dead based upon how much damage has been taken.  0 HP was the original transition point between being alive and being dead.  While there are variations across the editions on what happens when a creature loses HP, and what happens at 0 HP, this general concept has remained consistent.  For a proto D&D (pre publication) HP system, I have added a coda at the end of this answers.   
Starting in AD&D 1e, features were added (like negative hit points and bleeding out), death from massive damage (50 HP in one blow) in 2e, or subtracted (negative hit points removed in 2e), as game mechanics that went beyond the abstraction of how much damage it takes to kill the player character or creature.   
Until 4e, and now in 5e, restoring a character to full HP without using magical means (healing potions / spells) was a time dependent activity (down time) that required multiple long rests that could run into days or even weeks of in-game time (campaign time).  This mechanical effect suggests that from the beginning, HP were also a measure of general health and state of injury and not just the abstract “still fighting or down / dead” as HP are used in combat.       
OD&D
You’ll roll d6 for HP and like it!  

Dice for Accumulative Hits (Hit Dice):  This indicates the number of dice which are rolled in order to determine how many hit points a character can take. {snip} Thus a Super Hero gets 8 dice + 2; they are rolled and score 1, 2, 2, 3, 3, 4, 5, 6 / totals 26 + 2 = 28**, 28 being the number of points of damage the character could sustain before death.  Whether sustaining accumulative hits will otherwise affect a character is left to the discretion of the referee**.  (Men And Magic, p. 18).    

A Constitution of 15 or greater added +1 point per HD.  (Men and Magic, p. 11).   
Different HD and HP averages based on class arrived in the Greyhawk supplement. (Fom all characters using d6 to Fighter d8, Cleric d6, Magic User d4, and Thief d4)    

Alternate Hit Dice and Hit Point Accumulation: this system is expressly aimed at raising Fighters and lowering Magic-Users with regard to hit points which can be sustained.  This system functions as follows: for each level attained the character gets one die for hit points until the top normal level is reached; thereafter a certain number of hit points will be added for each level above normal that is attained. (Greyhawk, p. 10).  

Differing sized HD to determine HP for each class has remained the standard in all subsequent editions, although the actual sized HD each class uses has changed in some editions.  Any class with a Constitution of 15/16, 17, or 18, could accrue +1, +2, or +3 HP respectively per hit die. (p. 9, Greyhawk)     
An early “HPs are also about health and injury” optional rule: hit location     

DAMAGE ALLOCATION
  HEAD (15%), CHEST (80%), ABDOMEN (60%), ARMS (20%), LEGS (25%), TAIL (20%), (optional), WINGS (10%) (optional) (Blackmoor; page 7 and 8)   

The above option assigned a number of hit points to a body part and included a table to indicate which body part was struck during combat.  Note that if you add it all up it is greater than 100% of the HP total of the creature.  (Our group tried it and discarded it as too much trouble).  In this optional approach, for example, if your head took more damage from an attack than it had hit points the creature died -- even if it was the first blow struck in the battle!  Later versions of "it's all over with one hit" are seen via massive damage in 2e and 3.xe, and the use of the critical hit feature.    
I bring up this early mechanical / health linked HP scheme to illustrate a point: there has always been an idea that HP should reflect overall health and state of injury, which other game systems also used (Runequest being one example).  A "healing wounds" time-related HP recovery mechanic persisted from OD&D until 4e, via the direct linkage between HP and health / injury when restoring a character to full HP after an adventure.    

HEALING WOUNDS
  As noted previously, energy levels can only be regained by fresh experience, but common wounds can be healed with the passage of time (or the use of magics already explained). On the first day of complete rest no hit points will be regained, but every other day thereafter one hit point will be regained until the character is completely healed. This can take a long time.  (Wilderness and Underworld Adventures, p. 35).   

Holmes / Basic D&D
The blue book retained the OD&D HP system.   The treatment is brief (page 7; discussion on which dice size each class uses removed, but each class used a different hit die):   

First, generate a random number for "hit points."  {snip} This
  represents the amount of damage the character can take.  {snip} In
  combat, if a character receives a blow, a dice roll will be made to
  determine the number of damage points inflicted. These are subtracted
  from a character's "hit points." If his score falls to zero he is
  dead.  {snip}Each day of rest and recuperation "back home" will
  regenerate 1 to 3 of his hit points for the next adventure.  

AD&D 1e
In E.G.G's (overly verbose) style ...   

These hit points represent how much damage (actual or potential) the character can withstand before being killed.  A certain amount of these hit points represent the actual physical punishment which can be sustained. The remainder, a significant portion of hit points at higher levels, stands for skill, luck, and / or magical factors.  {snip}  Let us suppose that a 10th level fighter has 55 hit points, plus a bonus of 30 hit points for his constitution, for a total of 85 hit points.  This is the equivalent of about 18 hit dice for creatures, about what it would take to kill four huge warhorses. It is ridiculous to assume that even a fantastic fighter can take that much punishment.  The some holds true to a lesser extent for clerics, thieves, and the other classes.  Thus, the majority of hit points are symbolic of combat skill, luck (bestowed by supernatural powers), and magical forces.  (PHB p. 34)   

Constitution Bonuses for HP.  (A Fighting Man could get +3/+4 with an 17/18 Con)   

Note also that the only class of characters which is entitled to bonuses above +2 per hit die is fighters (Including the fighter sub-classes paladins and rangers).  Thus, even though a cleric, magic-user, or thief has a constitution of 17 or 18, the additional hit points for each hit die due to superior constitution is +2. (PHB p. 12)  

A further explanation of why high level characters have more HP:  

Consider a character who is a 10th level fighter with an 18 Constitution.  This character would have an average of 5.5 hit points per die, plus a constitution bonus of 4 hit points, per level, or 95 hit points!  Each hit scored upon the character does only a small amount of actual physical harm - the sword thrust that would have run a 1st level fighter through the heart merely grazes the character due to the fighter's exceptional skill, luck, and sixth sense ability which caused movement to avoid the attack at just the right moment.   However, having sustained 40 or 50 hit points of damage, our lordly fighter will be covered with a number of nicks, scratches, cuts and bruises. It will require a long period of rest and recuperation to regain the physical and metaphysical peak of 95 hit points. (DMG p. 82)  

The long recovery time to get back to full HP carried over from OD&D in this edition, and was retained in 2e.  In 3.xe you recovered 1 HP per character level per long rest (without magical healing), while in 4e or 5e a long rest restores max HP.    
Introducing negative hit points:  

Zero Hit Points: When any creature is brought to 0 hit points (optionally as low as -3 hit points if from the same blow which brought the total to 0), it is unconscious.  In each of the next succeeding rounds 1 additional (negative) point will be lost until -10 is reached and the creature dies.  Such loss and death are caused from bleeding, shock, convulsions, non-respiration, and similar causes. It ceases immediately on any round a friendly creature administers aid to the unconscious one.  Aid consists of binding wounds, starting respiration, administering a draught (spirits, healing potion, etc.), or otherwise doing whatever is necessary to restore life.  DMG p. 82)   

Why do I mention this feature?  In the negative HP mechanic, which we also see in 3.x, HP as health during combat differs from the original system of "alive" or "dead."  It allows hope of survival after being reduced to 0 HP, so the negative HP represent someone dying/bleeding to death due to injury, rather than the "alive / dead" method previously used, and used again in AD&D 2e where > 0 HP means you are alive, and <= 0 HP means you are dead.   
BX/BECMI;
Moldvay on page B6: Hit points and Hit Dice    

Hit points represent the number of points of damage a creature or
  monster can take during battle before dying.  Any creature reduced to
  0 hit points (or less) is dead.

Restoration of HP without healing spells/potions was at 1-3 P HP per day of rest. (B 25)  
Rules Compendium(BECMI)  

Roll for Hit Points
  Your character's hit point score represents his ability to survive injury. The higher his hit point score, the more damage he can sustain before dying. Characters who survive long enough to gain a good deal of experience typically gain more and more hit points; therefore, an experienced character lasts longer in a fight or other dangerous situations than does an inexperienced character.  

Death Saving Throws showed up (p. 266 Variant Rules): for players reduced to 0 HP where raise dead/resurrection spells are not available, or not in the game, this "save versus death ray" from the saving throw tables allowed the party to try and keep the character alive and to apply healing before death became final.
Constitution bonuses were not restricted by class: 13-15/16-17/18 offered +1/+2/+3 HP per level respectively.   
AD&D 2e
Character Death returns at 0 HP.  

When a character reaches 0 hit points, that character is slain.  The character is immediately dead and unable to do anything unless some specialized magical effect takes precedence. (DMG p. 154)  

Beyond the "at 0 HP you are dead" principle was some explanation:   

To allow characters to be heroic (and for ease of play) damage is handled abstractly in the AD&D game.  The more HP a creature has, the harder it is to defeat.  The damage isn't applied to the head, or divided among different areas of the body.  (PHB p. 209).  {This looks like a passing reference to the Blackmoor option I noted above, and to other games of the time (like Runequest) that used a hit location scheme}.    

2e added death from massive damage 

In addition to dying when hit points reach 0, a character also runs the risk of dying abruptly when he suffers massive amounts of damage.  A character who suffers 50 or more points of damage from a single attack must roll a successful saving throw versus dead, or he dies.  This applies only if the damage was done by a single attack. (DMG p. 154, PHB p. 209)  

This is a change in scheme from the previous editions.  I don't find a "massive damage" passage in the 1e DMG.   
The "negative hit points" feature was removed.  (But it didn't stay dead!)  
Constitution bonus for a Constitution above 16 (+2) remained restricted to the Warrior class only. (Fighter, Ranger, Paladin).    
Natural Healing (HP recovery) was 1 HP per day, 3 HP per day with bed rest, and addition of constitution bonus for each week of bed rest.  Like in 1e and OD&D, recovering HP took a long time in-game unless magically assisted.  (PHB p. 213)   
D&D 3.xe
Restored negative hit points, and provided a different recovery mechanic.   

Your hit points measure how hard you are to kill.  No matter how many hit points you lose, your character isn't hindered in any way until your hit points drop to 0 or lower.
What hit points represent
  Hit points mean two things in the game world: the ability to take physical punishment, and the ability to turn a serious blow into a less serious one. {Massive damage in this edition is similar to 2e edition, with 50+ HP in one blow causing a death save (Fortitude, DC 15)} d20SRD, Injury and Death. 

3.x used the negative hit point feature we first saw in AD&D 1e to include the limit of -9 before a chance to heal / save the character is no longer viable.   This negative HP mechanic (loss of 1 HP per round until one reached -10*aka*dead was not used in the other systems besides 1e.  The "Dying" condition was when you had from -1 to -9 HP.  (d20srd; Conditions; Dying).   
Natural Healing was at 1 HP per level per day. 
D&D 4e
HP is a combination of factors that makes a character harder or easier to kill.  

"Hit points (hp) measure your ability to stand up to punishment, turn deadly strikes into glancing blows, and stay on your feet throughout a battle. Hit points represent more than physical endurance. They represent your character’s skill, luck, and resolve — all the factors that combine to help you stay alive in a combat situation." (4e, PHB, p. 239, thank you @mattdm)  

4E has the "bloodied" condition which is when the PC is at one-half of max HP or less.  At this point, you (or a monster) are visibly wounded. A bunch of game-mechanical stuff triggers off of this condition.  This choice added mechanical effects before the creature got to 0 HP or below that isn't present in the other editions.  
Natural Healing: Characters restore maximum HP on a long rest.  On a short rest (five minutes or so) they can spend as many Healing Surges as they have available (Healing Surges are replenished upon long rest, being based on both class and Con score; each surge is equivalent to 1/4 of max HP).  
Negative HP are a thing, however they were differently implemented than in 3.x or 1e.  Your negative HP limit was your "negative bloodied" (one half your max HP, negative) beyond which you died.  A healing effect (like a cure wounds spell) restored you to 0 HP plus the amount healed(Thanks, @kviiri).   How HP works in 4e is succinctly described here by @waxeagle.  To a certain extent, being at 0 HP and negative HP (up to your negative bloodied limit) were the same thing: you were dying but not dead yet2.  
D&D 5e
Same basic principles, and another variation on what happens at 0 HP.  

Hit Points and Hit Dice
  Your character’s hit points define how tough your character is in combat and other dangerous situations.  Your hit points are determined by your Hit Dice (short for Hit Point Dice). (Basic Rules p. 7.)   

In this edition, as in 3.x, 4e, and in BX/BECMI, Constitution bonuses are not restricted at the higher scores by class as they were in AD&D 1e and 2e.
Hit Points 

Hit points represent a combination of physical and mental durability, the will to live, and luck.   Creatures with more hit points are more difficult to kill. Those with fewer hit points are more fragile.  A creature’s current hit points (usually just called hit points) can be any number from the creature’s hit point maximum down to 0. This number changes frequently as a creature takes damage or receives healing.  Whenever a creature takes damage, that damage is subtracted from its hit points. The loss of hit points has no effect on a creature’s capabilities until the creature drops to 0 hit points. (Basic Rules p. 74).  

The mechanical impact of losing some, but not all, HP in 4e was removed.  The negative HP "you are not quite dead yet" feature is he use of "death saves" at 0 HP(which is similar to 4e2), and the "instant death" is a variation on the massive damage rule that 2e introduced.        

Instant Death
  Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum. (p. 75 basic rules)  

Instead of an absolute value from 2e and 3.5e(50 or more HP), the "big blow just kills you" mechanic is now measured against both your maximum HP and how you're doing so far in a given battle.  (Also similar to being reduced beyond negative 1/2 bloodied in 4e).      
Natural Healing is all HP recovered on a long rest, with HD available (based on level) to spend to restore HP during a short rest.  One half of your HD are restored to that function per long rest.  This is a variation on the feature 4e introduced with healing surges.  These two editions (4 and 5) disconnect HP recovery from injury/health seen in OD&D, AD&D 1 and 2, as well as 3.x, by not requiring time/magical healing to restore a character to full HP.     

1 For the sake of brevity, I do not include the Chainmail hit dice system that preceded OD&D.
2 At 0 HP in 4e 

If you fall under 0 hit points, you're unconscious and dying.  Every turn in combat, make a saving throw.  10+ and you don't get worse; 1-9, and you get one strike.  Three strikes, and you're dead.  Roll a 20, and you get to use a healing surge!  Oh, the negative-10-and-you're-dead thing changed. Now you get to go negative equal to your "bloodied" value, which is half your maximum hit point total. 

Proto D&D Hit Points
Before D&D was first published, there is some detail from a blog that has access to some pre published material and notes that are directly linked to the "18 pages of notes" that Arneson provided to Gygax that ended up turning into 3 little brown books.  Based on the research that this author has done, and a bunch of original source material, it appears that Greg Svenson (one of Dave Arneson's players) took notes on the early Blackmoor 'at the table play' in the back of his 2d edition Chainmail book. {All italics and bold are mine.}  

We are not quite at the end of the story and this brings us back to yesterday’s discussion of Greg Svenson’s notes in the back of his 2nd edition CHAINMAIL.  Here is another section of those notes:
“Life and death:
  Mortal 7 pt. damage to kill
  Hero 14 pt. " " "
  Super Hero 28 pt. " " "
  Wizard 21 pt. " " "
  recover 1 pt./day 

Recovering 1 HP carried over into OD&D, shown in Book 3 as noted above. 

Become hero if possess magic equipment or survived several expeditions or become super hero if you kill 1000 points of anything. 

Commentary on the above note.   

Again we see "points" for both men and monsters as synonymous with what D&D calls hit points, demonstrating fairly conclusively that Blackmoor monsters had hit points too, but, just as interestingly, we also see them as synonymous with experience points.  It’s beautiful economy really.  There’s no calculating of experience points verses player level and all that jazz.  You simply keep a running tally of the number of hit points a player has “killed” and when they reach 1000 – bam new level.
  So to sum up, any given monster in Blackmoor has a point value which simultaneously represents how much it costs to purchase, how much damage it can take, and how much experience it is worth when killed.
http://boggswood.blogspot.com/2014/08/on-creation-and-evolution-of-hit-points.html

