What was island hopping?
The term “island hopping” is typically used with reference to World War II. Therefore, I have moved your question to that section and I will assume that you are asking about that war.
The island hopping strategy was used by the United States in its war against Japan in the Pacific. The US knew that, to win the war, it would have to at least threaten to invade the Japanese home islands. The problem was that Japan controlled many small islands between Hawaii and Japan and between Australia and Japan. If the US had attacked every Japanese-held island, the war would have taken a long time and casualties would have been much higher than they were. Therefore, the US generally used the island-hopping strategy. That is, they chose not to attack a number of islands, instead simply bypassing them and attacking islands closer to Japan. For example, the US never tried to invade the large Japanese naval base at Truk. Instead, it hopped past that group of islands and invaded Guam and Saipan in the Marianas instead. It left the Japanese on Truk to “wither on the vine” instead of expending the resources needed to invade that island group.
Rather than methodically fight and conquer one Japanese island at a time, General Douglas McArthur instituted the policy of "island-hopping". Certain strategic islands were identified to be occupied by the Allied forces, while the rest were left isolated. This not only economised the costs of men lost, but proved to be an aim that could be easily achieved by the Allies, since the Americans had command of the air and the sea.