When a pitcher throws a curve ball he grips the ball with his fingers to impart spin on the ball when he thows it toward the batter. This gives the ball two motions i.e. forword velocity and spin. If the spin axis is in the vertical plane (i.e. updown )the pitch will rise if it is spining clockwise (i.e. toward batter) and fall if counterclockwise(i.e. away from the batter). If the spin is in the horizontal plane clockwise spin will(i.e. toward the batter)the ball will cause the ball to move toward the 3rd base side of the batter. If the spin is clockwise (i.e away from the batter) the ball will move toward the 1st base side of the batter. The reason for the ball movement is the air is moving over one side of the ball faster then the other causing lift or a aerodynamic force in the direction of movement. This force is caused by the spin on the ball. Think about the air on one side as moving at the speed of ball forward velocity plus the spin velocity and the other side as moving at ball forword velocity less the spin velocity. Various grips, arm positions, release points will then make the ball look like it is a dancing curve.