The goal of the island hopping strategy used by the US during World War II was to gain control of Japanese Islands in order to set up military bases. The US went from island to island, defeating the Japanese military in order to set up landing strips for planes and bases. From there, the military would then go to another nearby island to do the same thing.
Slowly but surely, the US military kept getting closer and closer to mainland Japan. The control of the surrounding islands made it easier for the US to plan attacks on mainland Japan.