A draw in golf is a shot that moves in the direction of the golfer (as opposed to a fade, which moves away from the golfer). For example, in a right-handed golfer, a draw will curve to the golfer's left as he looks down the fairway, while a fade will curve to the right (both deviating from a straight, or linear, trajectory). This also puts some backspin on the ball, which causes it to stop shorter than a fade, which has forward spin. A rolling draw describes a shot with draw that "releases" on impact and rolls forward farther than a normal draw.
5 Golf hit (the ball) so that it travels slightly to the left (for a left-handed player, the right), usually as a result of spin given to the ball: he had to learn to draw the ball—not least for the tee shots at Augusta.
• Billiards impart backspin to (the cue ball), making it move backwards after hitting an object ball. [NOAD]
It is useful to note the meaning in billiards, since they derive from the same idea, of putting backspin on a ball.