Q:

Is there a guide/convention to the markup being used in the lua official documentation?

I consistently have a really hard time reading official documentation when it's related to coding. I generally don't understand it unless it's paired with an example. I am seeking clarification on what kind of conventions are inplace when reading docs, if any. Take the example below from the lua manual(https://www.lua.org/manual/5.1/manual.html#2.1)
:
stat ::= if exp then block {elseif exp then block} [else block] end

The first word, Stat, is defined as a statement and "this set includes assignments, control structures, function calls, and variable declarations." 
::= Is not defined in the docs, it can be googled thankfully.
Exp is linked and explained. 
Block has a section as well.
But then they do {} and []. They literally stated "Square brackets are used to index a table" just a few lines above. And that squiggly brackets are for writing a table. So what am I supposed to deduce from this? That {} and [] are being used to denote separate sections as a markup to make it easier to see certain components? Or that {elseif exp then block} is a table with those values inside of itself and [else block] is a key-value indexing a table? If I was writing a doc where that was indeed the case, wouldn't I write it this way?   
Then I see 
var ::= prefixexp `[´ exp `]´`

' ' defines a string, but I have to make the assumption that '[' ']' is used as a way to highlight the fact that because they were talking about what square brackets do in the previous section they are simply highlighting their position and this should not be included in the code. I only know to make this assumption though cause I know it doesn't work when you put them in there.
But then I see this:
chunk ::= {stat [`;´]}

Similarly they are talking about the placement of the semicolon before listing that code, but the entirety of the line of code was also newly explained and being talked about. Why would I assume that its written without the parenthesis if its written with the parenthesis? And I see they are using {} and [] again, and I have no idea what they are referencing because its not stated explicitly that we're talking about a table...its simply using the code itself to explain whether its talking about a table or not with the {}, but we have that first set of code where {} is being used and its not talking about a table.
What is the convention being used? What are they actually trying to do/show by using {} and [] in the first line of code?

A:

As stated both at the beginning of the Lua documentation and in the section on the Lua grammar, Lua presents its grammar in extended BNF format.
EBNF has its own punctuation with its own meaning, like ::= as you discovered. But as a grammar, there needs to be a distinction between the EBNF meaning of a piece of punctuation and "this punctuation appears in the language defined by the grammar". The former meaning is therefore always assumed; the latter meaning can only be achieved by quoting the punctuation.
So this:
var ::= prefixexp `[´ exp `]´`

Means a prefixexp followed by an open bracket followed by exp followed by a close bracket.
By contrast, this:
funcname ::= Name {`.´ Name} [`:´ Name]

Means Name followed by zero or more sub-sequences of . followed by Name, followed by an optional sub-sequence of : followed by Name. Because those are what {} and [] mean to EBNF.

