What if I have 7 things and want to add 0 things to them?
The most obvious answer is that it doesn't change the amount of things I have.
This way, we can write:
$$7 + 0 = 7$$
How about the case where I have 22 things and want to add 0 things to them?
The answer is, of course, the same:
$$22 + 0 = 22$$
It seems obvious that this happens with any number.
We can write this down as
$$\text{any number I choose} + 0 = \text{the same number, it doesn't change}$$
That's quite a long line!
I think you can imagine that people who write a lot of mathematics get tired of such things really quickly.
This is why we abbreviate!
How should we abbreviate this line?
Well, the most extreme way of abbreviating is by using single letters! Very radical!
We write things like:
$$a + 0 = a$$
This means that we take any number and call it \(a\) for short.
If we add zero to it, we get back the same number we chose originally, namely \(a\), since it doesn't change.
The choice of letters is completely up to you!
You don't even have to use letters (although that's the most common), you can use any symbol or word for abbreviation!
We could have very well written
$$N + 0 = N$$
where N is basically short for "any number".
This is how letters are used in math ^.^