Well, one of the nice things about forums is that you sometimes hear the same information from different people, just explained in different ways.
So heres my version...
Crossovers. Put simply, the split a "Full range" signal (a signal which has normal Bass, Midrange and Treble in it), and split it either 2 (rare), 3 (common), or 4(fairly rare) ways.
Firstly, there are "Passive crossovers." These have no mains supply, and are mainly just a few coiled components mounted on a circuit board. These are commonly found inside speaker cabinets and take the full range signal from your amplifier and send the deep, low, bass notes to the woofer in the cabinet, and send the high, treble, top end sounds to the cabinets tweeters, and the middle frequencies go through to the midrange driver in the cabinet (This would be a 3-way crossover then)
Secondly, theres Active Crossovers. These are most commonly seen in 19inch wide, rackmount units. These again can be found in 3way or sometimes 4way versions. The BIG difference is that these normally work on the signal coming from your mixer, NOT the powerful signals coming out of you amps... 3 way Active Crossovers still split the mixer level signals into 3 mixer level outputs, which you then connect to your 3 amplifiers respectively. So, you'll have a Bass Amp, a Midrange Amp, and a high Amp. The amps dont have to be special, they can be 3 identical amps.
Rackmount active crossovers nearly always have front panel controls, but occasionally internal controls to adjust which groups of frequencies the unit should send to the BASS output, the Midrange output, and the Treble outputs respectively.
Some Crossovers may also incorporate additional features such as Compressor, or limiter circuits.
It is critical NOT to feed an active crossover with SPEAKER LEVEL signals from the REAR of an amp...unless you want to add pyrotechnics to your show.
(There is the slightest possibility that I've got Passive and Active around the wrong way... but the descriptions are valid...I think)
I just call mine "The crossover".
A rare, third type of crossover is also seen occasionally.
Some speaker systems offer a dedicated crossover, made by the same company who makes the speakers, which they often call a System Controller, or Black Box. These are commonly a 2 way active crossover, which works specifically with certain models of their cabinets.
The famous Bose 802 speakers often had their bass enhanced by a the Bose 402 Bass cabinets, and a little black box device (Bose System Controller) split the signals accordingly.
My own Ramsa speaker system (made by Panasonic/Technics) uses a similar amp level device to split the full range signal from mixer, into Bass (mono) and then Midrange/top(combined) Left and Midrange/top(combined) right respectively. Those 3 outputs go to the BASS amp (mono) and the left and rights of my stereo amp.