What exactly does the crossover do and how does it work with components?

 

Most mids are only capable of accurately reproducing the frequencies from about 100 Hz to about 3000-4000 Hz. And tweets from 3000-4000 up to near your human limit of 20000 Hz. The crossover is responsible for limiting the frequencies that are sent to the individual speaker drivers. And a crossover also limits the frequencies that are sent to a sub to help keep the soundstage up front. Otherwise the 80-2000 Hz range that the sub can reproduce would definitely sound like it's coming from the trunk with the 100-2000 watts sent to most subs.