The club heads travel must have a stable center for the path and the depth of the arc to be controlled. The perfectly controlled arc determines the direction of the club heads travel and the place on the club face where the ball impacts.
Just as the pin of the compass must remain in the hole in the paper for the pencil to return to the exact spot it started from to complete the circle. If we can maintain a fixed in space swing circle center we will both have much more accurate and solid club ball contact, as well as more club head speed.
An illustration of why we have more club head speed can be felt an seen by twirling a weight on a short (one foot) piece of string. Try this; swing a weight, a keyring works fine, move your hand in a good sized circle and gradually make the center of rotation as small as you can. You will find that when the center of the arc moves as you swing the weight the weight goes slowly, as the arc gets tiny the weight is literally zooming around.
Just as an unbalanced wheel can not be spun as quickly as a balanced wheel can, the golf swing needs that kind of a stable center to both create speed and to also have the kind of precision contact we desire.
When we address the ball one of our most important duties is to locate the exact location of the swing circle center. We do this by using the club as part of the measuring tool (the other part of the tool is the correctly angled left arm) to precisely position it. This measurement, and the maintenance of it, is vital to the success of the shot.
If the swing circle center moves around we lose both speed and the ability to return to the exact spot we measured at address.