The term Island Hopping refers not to one single battle, but rather a strategy employed by the Americans as they pushed closer to Japan. The Japanese fortified every island possible between the United States and Japan and fought to the death to hold each island. Taking every island one by one would greatly slow the U.S. forces approach toward Japan and cost untold lives.
Rather than taking out each and every island in between our strongholds and Japan, the United States decided they would invade and decimate an island, skipping one and hitting the next. And while this left a nest of Japanese between American strongholds, the Japanese troops were without incoming supplies and effectively removed from the war. This strategy allow the United States to move across the Pacific more quickly and saved untold lives.