This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
Why brake in the turn? If all braking is done before the turn, speed
will be slower than necessary before the apex. Anticipating maximum
speed for the apex is difficult, and because the path is not a
circular arc, speed must be trimmed all the way to that point. Fear
of braking in curves usually comes from an incident of injudicious
braking at a point where braking should have been done with a gentle
touch to match the conditions.
Substantial weight transfer from the rear to the front wheel will
occur with strong use of the front brake on good traction just before
entering the curve. When traction is poor or the lean angle is great,
deceleration cannot be large and therefore, weight transfer will be
small, so light braking with both wheels is appropriate. If traction
is miserable, only the rear brake should be used, because although a
rear skid is recoverable, a front skid is generally not. An exception
to this is in deep snow, where the front wheel can slide and function
as a sled runner while being steered.