Q:

What does fifth column of feColorMatrix stands for exactly

In mozilla's doc for feColorMatrix it is stated that

The  SVG filter element changes colors based on a
  transformation matrix. Every pixel's color value (represented by an
  [R,G,B,A] vector) is matrix multiplied to create a new color.

However in feColorMatrix there are 5 columns, not 4. 
In an excellent article that can be considered as a classical reference it is stated that:

The matrix here is actually calculating a final RGBA value in its
  rows, giving each RGBA channel its own RGBA channel. The last number
  is a multiplier.

But that does not explain a lot. As far as I understand, since after applying filter we basically modify exactly R, G, B and A channels and nothing else there's no need in this additional parameter. Indirectly there's an evidence for that in the article itself - all numerous examples of feColorMatrix-based filters provided - all have zeroes as fifth component. Also, why it's a multiplier? 
In another famous article it is stated that:

For the other rows, you are creating each of the rgba output values as
  the sum of the rgba input values multiplied by the corresponding
  matrix value, plus a constant.

Calling it a constant added makes more sense than calling it a multiplier, however it's still unclear what does fifth component in feColor matrix stands for and what is unachievable without it  - so that would be my question. 
My last hope was the w3c reference but it's surprisingly vague as well.

A:

The specification is clear although you do need to understand matrix math. The fifth column is a fixed offset. It's useful because if you want to add a specific amount of R/G/B/A to your output, that column is the only way to do it. Or if you want to recolor something to a specific color, that's also the way to do it.
For example - if you have multiple opaque colors in your input, but you want to recolor everything to rgba(255,51,0,1) then this is the matrix you would use. 
0 0 0 0 1.0
0 0 0 0 0.2
0 0 0 0 0 
0 0 0 1 0 
aka
<feColorMatrix type="matrix" values="0 0 0 0 1   0 0 0 0 0.5   0 0 0 0 0  0 0 0 1 0"/>

Try out these sliders for yourself:
https://codepen.io/mullany/pen/qJCDk

