A cut shot is usually played in order to get the ball around some obstruction in its flight path. For example, your drive lands on the right side of the fairway, where overhanging branches pose a problem. A cut shot will start the ball out to the left - going around the problem - before moving the ball back to the right.
Cut shots are frequently played on approaches to the green, as well, as a way of avoiding greenside hazards. For example, a right-handed player facing a green that is well-protected on the right but open on the left might to play a cut shot, bringing the ball into the green from left-to-right.
Cut shots are played either by opening the club at impact, or by swinging on an outside-to-inside swing path. A more severe cut shot might involve both maneuvers.
