This article is from the Car Audio FAQ, by Ian D. Bjorhovde (firstname.lastname@example.org) with numerous contributions by others.
A crossover is a device which filters signals based on frequency. A
"high pass" crossover is a filter which allows frequencies above a
certain point to pass unfiltered; those below that same point still get
through, but are attenuated according to the crossover slope. A "low
pass" crossover is just the opposite: the lows pass through, but the
highs are attenuated. A "band pass" crossover is a filter that allows a
certain range of frequencies to pass through while attenuating those
above and below that range.
There are passive crossovers, which are collections of purely passive
(non-powered) devices - mainly capacitors and inductors and sometimes
resistors. There are also active crossovers which are powered
electrical devices. Passive crossovers are typically placed between
the amplifier and the speakers, while active crossovers are typically
placed between the head unit and the amplifier. There are a few
passive crossovers on the market which are intended for pre-amp use
(between the head unit and the amplifier), but the cutoff frequencies
(also known as the "crossover point", defined below) of these devices
are not typically well-defined since they depend on the input impedance
of the amplifier, which varies from amplifier to amplifier.
There are many reasons for using crossovers. One is to filter out deep
bass from relatively small drivers. Another is to split the signal in
a multi-driver speaker so that the woofer gets the bass, the midrange
gets the mids, and the tweeter gets the highs.
Crossovers are categorized by their order and their crossover point.
The "order" of the crossover indicates how steep the attenuation slope
is. A first order crossover "rolls off" the signal at -6dB/octave
(that is, quarter power per doubling or halving in frequency). A
second order crossover has a slope of -12dB/octave; third order is
-18dB/octave; etc. The "crossover point" is generally the frequency at
which the -3dB point of the attenuation slope occurs. Thus, a first
order high pass crossover at 200Hz is -3dB down at 200Hz, -9dB down at
100Hz, -15dB down at 50Hz, etc.
It should be noted that the slope (rolloff) of a crossover, as defined
above, is only an approximation. This issue will be clarified in
future revisions of this document.
The expected impedance of a passive crossover is important as well. A
crossover which is designed as -6dB/octave at 200Hz high pass with a 4
ohm driver will not have the same crossover frequency with a driver
which is not 4 ohms. With crossovers of order higher than one, using
the wrong impedance driver will wreak havoc with the frequency
response. Don't do it.