It helps to think of the bicycle/motorcycle as an inverted pendulum. To sustain an acceleration in a given (lateral) direction, it must lean in that direction.

It helps to think of the bicycle/motorcycle as an inverted pendulum. To sustain an acceleration in a given (lateral) direction, it must lean in that direction. Countersteering helps to control/initiate the lean angle. To lean to the right, the rider steers to the left and the wheels (at the bottom) move to the left while the centre of mass stays where it was initially, thus the angle begins to lean to the right, initiating a steady rightwards acceleration.