Check out this page:
http://www.linkwitzlab.com/phs-dist.htm
I think it'll answer all of your questions.
When HeadRoom speaks about incoherence, I think theyre refering to distortion. As for a crossover, it just filters specific bands of frequencies. For example, if you had a cone tweeter, and a 6" woofer, you might want to cut off low frequencies from that tweeter at 1100hz. You'd use a capacitor to do this. For the woofer, you could simply use a inductor to filter out the high frequencies and cross it over at 1100hz as well. This is a simple example of a crossover. Many are more complex. The more complex the crossover, the more phase incoherence occurs in the circuit. Not only does this contribute, though, but so can resonances with the cabinate, placement of the drivers, etc.
The problem is, most phase distortions normally encountered, arent audible. Or atleast, arguably so, unless the distortion is gross.