No no no... let me explain this a little better.
A crossover divides up frequencies. A crossover acts like a separator for frequencies. Depending on how you set the crossover (if there is a way... some are factory set), low frequencies will go one way (to your sub), and the high frequencies will go another (normal speakers). You use a crossover to get the max out of your speakers without damaging them.
Bass speakers are made to respond to low frequencies and vice versa for tweeters/drivers (they are made for high frequencies). So if you didn't have a crossover, and you were sending low frequencies to a speaker that couldn't handle it, then it would distort, pop, or damage the speaker itself. To prevent that, you use a crossover to send the low freq's to a speaker that CAN handle them.
Kinda hard to explain, but that is a pretty good explanation.