A cyclist leans inwards when he is negotiating a curve so that

The weight W, acts vertically downward and the normal force, N acts vertically upward. The frictional force, F, of the road acts horizontally in the direction of which the cyclist is turning. The frictional force provides the centripetal force necessary to turn the cyclist. But the frictional force also produces a torque that will cause the rider and bicycle to tip outwards. When the cyclist lean inwards the normal force of the road does not act through the center of gravity thus producing an opposite torque that cancels out the torque provided by the frictional force. Thus there is no tendency for the cyclist to tip outwards.