+10 internets to those who know what a crossover is
In simple terms, a crossover is an electronic filter that rolls off (reduces) unwanted frequencies to a speaker. There are typically 3 types:
1. high pass - where the filter "passes" high frequencies and rolls off lower frequencies
2. low pass - where the filter "passes" low frequencies and rolls off higher frequencies
3. band pass - where there is both a "high" and "low" setting, creating a pass-band of frequencies (advanced - more to come)
4. subsonic filter - essentially a high pass on the lowpass (or a super low frequency bandpass, whatever is easier to understand). It filters low frequencies BELOW a certain point (usually very low). This prevents a sub driver from trying to play audio in a range it simply cannot, and hurting itself. Critical in vented applications with any sort of power since 1 octave below tuning the vent unloads and allows flopping. This filter protects you from that.
5. slope - the rate of rolloff on a particular filter - expressed as db/oct. Four typical slopes are 6/12/18/24 db per octave. Naturally a 12 db/oct slope is twice as steep as 6 db/oct. Each slope has its own effect on phase, but thats for another time General rules of thumb:
Set your filter slightly higher or lower than the designed frequency range of the driver. Typical consumer front speakers will work well around a 100hz highpass setting (that is, it allows all higher frequencies and rolls off lower frequencies starting at 100 hz). Typical consumer subwoofers in sealed/vented enclosures are usually happy between 80 and 100 hz low pass. On vented subwoofers set the subsonic filter (if you've got one) to about 20 hz to start. There is zero effect on output with a crossover - its strictly controlling what portion of the audio spectrum each set of drivers is allowed to see - noticeable changes in output are noticed because the driver is allowed to (or filtered from) playing in its happy place. Now the interesting part:
You can actually make things sound worse (way worse) by not setting these correctly. For example - if you have a particularly weak front end (or its overdriven and you're trying to compensate by setting xover much higher than optimal) you'll leave a giant hole in the freq response. Crossing your front end (assume a decent coaxial set of speakers) at 150 or 200 hz and your subwoofer set at 80 hz leaves a giant "hole" between them. From 200 to 80 hz will be very attenuated output - to a trained ear will sound flat and missing, and likely identify whats wrong right away. To the untrained ear, it'll just sound "bad".
IMHO the difference between a good system and a great one is MIDBASS. Those magical frequencies between roughly 50 hz and 200. The ones sadly lacking in most sound systems. You can see above by incorrectly setting xovers can create a bad hole right in this range - you may unknowingly be making things sound worse by crossing over too aggressively.
Gain and crossovers go hand in hand. If your gain is incorrectly set, you'll be tempted (or forced) to compensate for it with more crossover. In essence, you end up over driving a section of the system, and then "back it out" with crossover. As such, the first step to proper setup is gain. When we don't have all the artifacts of clipping of being over driven, its easier to set the crossovers lower to allow more overlap and things to sound fuller.