This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
Countersteer is a popular subject for people who belatedly discover or
rediscover how to balance. What is not apparent, is that two wheeled
vehicles can be controlled ONLY by countersteer, there is no other
way. Unlike a car, a bicycle cannot be diverted from a straight path
by steering the wheel to one side. The bicycle must first be leaned
in that direction by steering it ever so slightly the other way. This
is the means by which a broomstick is balanced on the palm of the hand
or a bicycle on the road. The point of support is moved beneath the
mass, in line with the combined forces of gravity and cornering, and
it requires steering, counter and otherwise. It is so obvious that
runners never mention it, although football, basketball, and ice
hockey players conspicuously do it.