$\color{purple}{a+0=a}$

What does it mean?

It means, that addition of zero to the number will not change the number.

Indeed, suppose your first friend (let's call it Tom) gave you 3 apples, but your second friend (let's call it Jim) gave you nothing. So, you are left with 3 apples.

Using commutative property of addition, we can write that $a+0=0+a$.

Thus, $\color{purple}{a+0=0+a=a}$.

This is also true, if we subtract zero: $a-0=a$.

In fact, identity property is true for any real number.

Example 1. ${3}+{0}={3}$.

Example 2. ${\left(-\sqrt{{{2}}}\right)}-{0}=-\sqrt{{{2}}}$.

Example 3. ${0}+\frac{{5}}{{8}}=\frac{{5}}{{8}}$.

Conclusion. Addition or subtraction of zero doesn't change things.