It's the most used key on the keyboard.
Why space bar on the keyboard is bigger?
Because when you're typing fast, it makes it easier to hit when you're typing. It wouldn't make sense to have a tiny spacebar.
Bigger than the other keys? It's used after every word and that makes it easier and faster to hit.
Bigger than the space bar on another keyboard? There's no standard size. It's up to the manufacturer.