What do they do?
To understand how crossovers work, you first need to understand how sounds work. Imagine sounds as waves in water. When you toss a stone in water, ruipples or waves are created. These expand outwardly in a circular pattern. Just as with sound waves, when the ripples bump into anything they'll start off in another direction, and when they hit other they can overlap, cancel each other out, or if they're moving at the same speed, join together.  The more objects there are to hit, the more mess there is - so just think about your car's interior.

Now, if you lob a load of stones of different sizes in at once, you're going to have lots of large and small ripples or waves hitting each other. This is what happens when you play sound from your head unit. The frequencies are like the stones, all sent together at different volumes. Speakers cannot reproduce every single frequency at once because of their physical limitations. That is why we have subwoofers for bass or low frequencies, midrange speakers for mid-frequencies and tweeters for the high stuff. Because these speakers are designed to reproduce certain frequencies, we need to make sure they don't receive the frequencies they don't want by filtering them out. Crossovers are electronic audio filters. They work by splitting the sound frequencies into different bundles that can be sent to the correct speakers.

Crossover types
Passive crossovers
These are normally circuit boards made up from different electrical components such as capacitors and coils. They don't have an external power supply and are usually wired in between the amp and speakers. They are usually designed by the manufacturer for a specific set of speakers, such as components. 
Whether they're any good or not depends oon how much time and effort has been spent on making sure the design is correctly matched to the speakers. Because passive crossovers normally get their input signal from an amp, the signal is very high. But by the time it has passed through the circuitry, it can become reduced - negatively speaking, the speaker's output, know as insertion loss.
Also, the only way to release the unwanted signals or frequencies the circuit has filtered out is through heat. It's not uncommon to find passive crossovers have melted due to hard use.

Active crossovers
A crossover with a power supply is 'active'. They can either be seperate units or in-built into an amplifier. They work by filtering through the correct frequencies before they get amplified and then passed on to the speakers.
Because active crossovers have their own power supply, they don't suffer from insertion loss. In fact, many add gain to the signal - improving sound quality and volume.
The only drawback is that some active crossovers run two channels and some four. If you have a two-channel crossover, you'll have to buy one for each amp. However, this does give you flexibility with your ICE system.

Important features
An important feature to look at when buying a crossover is the 'slope'. We can measure the slope on a Real Time Analyser (RTA) - a device that uses a graphical display to show measurements of frequency in hertz (Hz).
If you imagine all the frequencies within the crossover's bandwidth as lines on a graph, you'd notice that as they got louder, the lines would slope upwards to one point - the cross over point (see diagram)

If the volume increased quickly, the slope of the lines would become steeper. This is what happens with crossovers. The more decibels (dBs) a crossover can increase the frequencies by per octave the better it is.
Most passive crossovers are typically 6-12dB/octave. Any more and the unit would cost too much and be huge. Some of them can be adjusted, but only slightly. Active crossovers have steeper slopes - a good thing as they allow you to get more out of your system without damaging anything. You should aim for at least 18dB/octave unit, or ultimately, a 24db/octave active unit.

Setting up
As with nearly all things to do with ICE, personal preference comes into play when setting up. Different elements, factors and components  in your system will affect the way your crossover is set up so there are no set rules. It's task that should be taken on by a pro if you have little understanding of the manual or how to connect one. If you do, there are basic guidelines to follow.
Low frequencies are more dangerous than high and reproducing lows takes more power from the amps and movement from the speakers. Check the recommendations for the frequency limits of the speakers and never attempt to play them outside these boundaries. When using a crossover with a steeper slope, you can play the speakers closer to their limits, with more power totally safely. Some crossovers can also vure acoustic 'nulls'. These occur when the same frequencies produced by two speakers start to collide into each other, cancelling each other out.
It sounds as though something is missing from the music and can be cured in two ways: either by moving the speakers (hard in a car); or by electronically adjusting the time alignment of the soundwaves.

Technical jargon explained
Subsonic filter
There's no point in you system using power to play subsonic frequencies because you can't hear them. A subsonic filter actually helps to eliminate them and free-up power.
Frequency The number of identical sound waves arriving at a point in one second. This measurement is expressed in hertz (Hz) or kilohertz (1kHz = 1000Hz).
Frequency spectrum
Treble (highs) : the top end frequencies, about 3kHz to 4kHz
Midrange (mids) : usually they key tones or vocal frequencies, ordinarily 300Hz to 400Hz to 3kHz
Bass (lows) : the low stuff, around 20Hz to 400Hz
Mid-bass : mid-level bass, normally 100Hz to 400Hz
Sub-bass : the very low stuff, usually from 20Hz to 100Hz
Subsonic : these are sound frequencies humans cannot hear, generally outside of 20Hz and 20kHz