In the above pictures, Jennifer Marshall shows the proper way to hold a ball.  The fingers should be comfortably spread on the ball with a 'pocket' between the ball and the palm.  This gives the bowler fingertip control of the ball at the release and provides both greater accuracy and more strikes.  The smaller the bowler's hand, the smaller the space will be between the ball and the palm.  Except for very small hands, the ball should not rest on the palm.