Why does a motorcyclist lean inwards while negotiating a curve?

To accommodate the acceleration.

Acceleration has direction and magnitude. When turning, the direction is constantly changing. If the cyclist does not lean inwards, the force from the acceleration would through him/her "out of the loop." So by leaning inwards, the cyclists center of balance is in a smaller radius than the wheels (which are the only things touching the ground). Thus, the force from the turn balances out with the bikers lean and friction of the wheels with the ground.

Click on the related link (Counter Steering, a motorcycle technique) below and there is a good explanation for this as well