Crossovers basically comes from the idea of crossing over from one frequency range to the next. It acts as a filter that blocks out unwanted frequencies to a speaker or group of speakers.
It is useful because it allows you to send each speaker the group of frequencies that it will play most efficiently and effectively.
The 3 basic ways a crossover will divide frequencies:
High-pass filter - filters higher frequencies to pass through to speakers
Low-pass filter - Filters low frequencies to pass through to speakers
Band-pass filter - A combination of a High and Low Pass Crossover to allow a range of frequencies above and below two chosen crossover frequencies.
There are 2 basic types of crossovers:
Electronic Crossover: An electronic crossover uses a DSP chip or Microprocessor to divide frequencies. Electronic Crossovers are typically more expensive than Passive Crossovers.
Passive Crossover: A Passive Crossover uses resistors, capacitors, inductors, or a combination of all three in order to achieve the desired crossover point for a speaker or group of speakers. Passive crossovers can be advantageous, since they are usually less expensive to produce and, in the case of component sets designed by a manufacturer, they offer you a great transition between tweeter and midrange… right out of the box. The disadvantage is that the filters themselves can be large, so they are typically intended for smaller speakers. Subwoofers, on the other hand, would require very large and heavy inductors to handle the necessary power and allow for only the low frequencies to pass through a smaller filter. Passive crossovers are often included with component and high-end coaxial speakers.