The Eccentric Edge Band ring has an offset hole so that a larger stone can be held than would normally be possible with a symmetrical ring.  On symmetrical rings, as stones get larger, the ring has to get thicker in order to accommodate the stone. The offset allows the fingers to stay closer together while still having the larger stone. The practical limit is around 5 to 5.5mm diameter stones with this style.  Other fully offset rings can handle larger stones.