Can someone explain what crossover is and how it's used?

A crossover basically splits a signal into 2 (or more) parts, based on frequency. Inside a 2-way speaker, for example, a crossover is used to direct the low frequencies to the woofers and the high frequencies to the tweeters. In a 3 way speaker, the crossover splits the signal 3 ways and sends it to the 3 drivers--woofer, midrange, and tweeter.
Crossovers are also used in bass management in Dolby Digital and DTS decoders in your receiver or pre-pro. If you set your speaker size to "small", frequencies below the crossover point are redirected to the subwoofer output. On many receivers, the crossover point is fixed (usually between 80 and 120 Hz), but some have a selectable crossover point to better match the capabilities of your speakers and sub.
So that's crossovers in a nutshell.
KJP

 

Also note that the cross-over is not a brick wall.
At the specified frequency, response will be down by some ammount (generally either 3 or 6dB). Beyond (higher for a low pass filter, lower for a high pass filter) that point, volume will be reduced by some amount (usually either 12 or 24dB/octave). Note that the high and low pass filters may have different slopes, and on THX equipment the 12dB/octave high pass is intended to sum with the speaker's natural roll off to create a 24dB/octave slope. An octave is a doubling or halving of frequency.
Put into practice with the stereotypical 12dB/octave cross-over at 80Hz:
At 20Hz, the main level will be 27dB down
At 40Hz, the main level will be 15dB down
At 80Hz, the mains and subwoofer will be playing the same signal. The level from each will be 3dB down from if you had the mains set to large.
At 160Hz, the subwoofer level will be 15dB down
At 320Hz, the subwoofer level will be 27dB down