Definition: A term applied to golf balls, compression is a rating of how dense a ball is. Another way of putting it: it's a rating of the softness or hardness of the ball. The side of the ball that is struck by the club will be literally squashed flat. The ball then springs back into shape. If a ball has a low compression rating - indicating a softer ball - it will be more easily "squashed" at impact. If a ball has a higher compression rating - indicating a harder ball - it will take much greater force to "squash" the ball at impact.
Players with slow swing speeds generally play softer balls (i.e., balls with a lower compression rating), while players with higher swing speeds generally play harder balls (higher compression rating).