A. The principle of physics at work in this phenomenon is Bernoulli's equation. The ball is released by the bowler in such a manner that it spins in air. The air near the ball is set in motion similar to that of the ball. The speed of air on one side of the ball increases and on the other side, the speed decreases.
So, in accordance with Bernoulli's equation, the pressure decreases on the side where speed is more and on the other side, it increases.
Thus, there is a net force on the ball towards the side of less pressure and it swings in that direction.
If the axis of spinning of the ball is parallel to its linear motion, it deviates sideways depending on the direction of spin. If the axis is horizontal and perpendicular, it deflects upwards or downwards and if the axis is vertical and perpendicular, the ball deflects sideways again.
Golf balls are dimpled to use the same effect to provide them with a lift in air.