This article is from the Car Audio FAQ, by Ian D. Bjorhovde (firstname.lastname@example.org) with numerous contributions by others.
For increased power. If your amp can handle the load, it will put out
more power through a bridged channel than it would into through a
non-bridged channel. Theoretically, a "perfect" amplifier that puts
out X watts into Y impedance into each of two channels will put out 4X
watts into Y impedance into one bridged channel. Be aware that some
amps more closely approximate that perfect amp than others, and some
manufacturers build current limiters into their amps to allow them to
remain stable into difficult loads at the expense of power gains.