it's used to divide a signal into frequency divisions.
to make sure that everything below say, 250 hz gets sent to the sub. everything between 250-4000 goes to the mid speakers and everything above 4000 goes to the tweeters.
A crossover just divides a frequency range at a definable/fixed point. It's useful for such things as driving a subwoofer (i.e. you don't want to send high frequency content to a sub) and bi-amped speakers (which have dedicated inputs for the tweeter and the bass driver).