It was actually used to reference the tightness of the windings around the center core of a three piece ball - the tighter the windings, the better the ball performed. This created a long-standing perception that compression affects golf ball distance and performance. Because golf ball technology uses newer heat-resistant threads with newer and better winding equipment for three piece balls, golf ball compression has become merely a condition of feel. And now with the availability of the consistent quality of a two piece ball, compression as a measurement of quality is just about obsolete. This number defines the deflection that a golf ball undergoes when subjected to a compressive load.
Compression simply measures how much the shape a golf ball changes under a constant weight.
Any balls that fall out of this range are usually discarded, sold as range balls, or sold as X-outs. There have been several published texts to prove that golf ball compression relates more to feel and your own superstition than its performance. The conclusions were, if you take different rated golf balls which have the same construction, aerodynamics, and cover material, and use an automatic golf swing machine such as the Iron Man, the yardage difference between the balls hit were negligible, less than two yards.