in a nutshell, a crossover is a like a filter for audio frequencies. It sends only certain frequencies to certain speakers, like vocals to tweeters and kick drums and bass beats to subs/woofers.

If your car has just full range speakers (read:stock) and/or an aftermarket head unit. you dont need a crossover, cuz the speakers have like some kind of passive crossover b/t the woofer and tweeter...or somehting.

however, if you have an amp bridged to a certain speaker (read:subwoofer) you might need a crossover, if your amp doesn't already have one (most do tho).