This article is from the rec.audio.* FAQ, by with numerous contributions by Bob Neidorff others.
Most speakers are connected to an amplifier by one pair
of terminals on each speaker. Within these speakers, a
crossover distributes the signal (modified appropriately)
to each of the drivers in the speaker.
Some speakers are set up to be either biwired or biamped. A
much smaller number allows triwiring and triamping. The same
principles apply but use three sets of wires or three amplifiers
instead of two. Most speakers that support biamping/biwiring
have two pairs of terminals and some mechanism for shorting
the two pairs together when used in the normal way. This
mechanism is most likely a switch or a bus bar. To help
the descriptions below, I will refer to these two pairs as
LO and HI (because normally one pair connects to the woofer
and the other pair connects to the tweeter/midrange).
Biwiring means that a speaker is driven by two pairs of wires
from the same amplifier output. One cable pair connects HI to
the amp, and the other cable pair connects LO to the same amp
output that you connected the HI cable to. Biwiring is
controversial; some folks hear a difference, some do not. One
plausible explanation for this involves magnetic induction of
noise in the relatively low current HI cable from the high
current signal in the LO cable. Accordingly, Vandersteen
recommends the two cable pairs for a channel be separated by at
least a few inches. In any case, the effect appears to be small.
Biamping means that the two pairs of terminals on a speaker are
connected to distinct amplifier outputs. Assuming you have two
stereo amplifiers, you have two choices: either an amp per
channel, or an amp per driver. For the amp per channel, you
connect each terminal pair to a different channel on the amp
(for example, the left output connects to HI and the right side
to LO). In the other configuration, one amp connects to the LO
terminals, and the other amp is connected to the HI terminals.
The point of biamping is that most of the power required to
drive the speakers is used for low frequencies. Biamping allows
you to use amps specialized for each of these uses, such
as a big solid-state amplifier for the LO drivers and higher
quality (but lower power) amp for the higher frequencies.
When you have two identical stereo amps, some folks
recommend distributing the low-frequency load by using an amp
per channel. In any case, whenever you use two different
amplifiers, be careful to match levels between them.
Biamping also allows you to use high-quality electronic
crossovers and drive the speaker's drivers (the voice coils)
directly, without the series resistance and non-linear
inductance of a passive crossover. Biamping which uses the
speaker's crossover is therefore much less desirable. Replacing
a good speaker's crossover with an electronic crossover has
advantages, but involves some very critical tradeoffs and tuning
which is best left to those well-equipped or experienced.
See also section 16.0 below, on wire and connectors in general.