Curl determines how much the trajectory of the shot bends so that it flies in an arc instead of a straight line.
The direction of your curl will also determine the direction that the ball travels in after landing.
Curled shots are useful for avoiding various obstacles on the course such as trees, bunkers, hazards, and for lining your trajectory up with curved fairways.
You can activate a curled shot by dragging the ball off to one side when powering up your shot.