A motorcycle rounding a curve has three forces acting on it. Imagine you are watching the motorcycle approach you while it is leaning to your left. The force of static friction points left and acts at the tire contact point. The NET of the three forces points left and is equal to the friction force, since the weight and normal force vectors add to zero.
Centripetal force is another name for the net force in situations involving circular motion.
If you turn the handlebars while going fast, the cycle will fall over away from the center of the curve as you steer. The front wheel precesses like a gyroscope , with the end of the axle pointing away from the center of the circle tending to drop downward. Leaning provides a steering effect without causing the motorcycle to flop over. In the diagram to the right, the center of mass of the cycle and rider is assumed to be positioned where the vectors r and mg meet.