Imagine you have a big ol' block of cheese. Someone comes along and leaves a quarter inch gouge in the top of it. But you want it to look whole again... for some reason.

You could painstakingly carve another piece of cheese into the shape that was gouged out and try to fill that gap, but that would be hard and probably wouldn't work out very well.

Or you could shave a quarter inch off the top of your block of cheese. Yes, your block of cheese won't be quite as large, but it'll look untouched once again, and with minimal effort on your part.

Sanding a scratch in paint is more or less the same. You're not "fixing" the scratch so much as removing the scratched layer of paint (or the clear coat on top of it). But this only works when the scratch in your paint is fairly minor. If it goes all the way through to primer or to bare metal, sanding obviously won't work.