This is an excellent question!
If I write \(x^2\) that 2 means I am really multiplying a number x by itself two times, like this \(x*x\) which you well know! So we have nice things such as let's say we want to multiply these numbers together:
\[x^2*x^3\]
We might not know, do we multiply or add the 2 and 3 together? Well one simple way to find out it to write it all out by what the 2 and 3 really mean, just multiply x by itself twice and multiply x by itself 3 times.
\[x^2 *x^3 = (x*x)*(x*x*x) = x*x*x*x*x = x^5\]
Ahhh so we see that the rule must be adding!
\[x^2*x^3=x^{2+3}=x^5\]
We can write this more generally as:
\[x^n*x^m=x^{n+m}\]
What if now we say m=0 in this formula?
\[x^n*x^0 = x^{n+0}\]
We see that this is really just:
\[x^n*x^0=x^n\]
So we must accept that \(x^0=1\), because we know \(x^n*1=x^n\). But this is still unsatisfying to us! What does this mean? We can see that it must be true, but why is it so?!
Let us again think back to our definitions. We know that \(x^2\) just means x multiplied by itself twice. What about \(x^1\)? This is just x multiplied by itself 1 time, which seems weird to say, but we can probably accept that it just means one x. Now how about \(x^0\)? This means x multiplied no times! That means there aren't even any x's there.
You will say, "This too is unsatisfying!" and I agree with you. Maybe we can't understand such a thing from this perspective? By analogy with physics, not even Einstein understood gravity! He only ever was able to describe how it behaves by imagining gravity as a curvature of space. Maybe at the end of the day, nothing is truly understandable? Or maybe we just haven't gotten to the bottom of it yet.