It is unfortunate that the answer by "larrygates" has been allowed to stand for four years, as it is fundamentally misleading with regard to the reason for the "island-hopping" strategy pursued by the United States in the war against Japan. The "island-hopping" strategy was not pursued because of the fanatical determination on the part of the Japanese soldiers who defended the series of small islands whose cost of conquering was astronomical in numbers of lives (over 111,000 American soldiers were killed in the battles to secure the chain of islands leading to the Japanese mainland, with tens of thousands more allied soldiers also killed). The strategy was pursued because of the limitations of the American bombers that existed during much of the war. Those limitations involved the range of the aircraft, which was too short to allow for the bombing of Japan from safer, more remote airbases. The islands had to be taken from their Japanese defenders so that airbases could be built that would allow American aircraft to reach closer and closer to the heart of Imperial Japan. B-25 bombers were very limited in range, and it wasn't until the introduction of the B-29 Superfortress that American bombers were able to reach Japanese targets from a greater distance. The series of airbases that were constructed with the invasions of the chain of islands leading closer and closer to the Japanese mainland were instrumental in facilitating direct bombing raids over Japan, and that was the reason for island-hopping.
In the end, of course, the Japanese emperor was compelled to surrender only after the atomic bombings of Hiroshima and Nagasaki in August 1945, the American aircraft having taken off from the very islands captured in the island-hopping strategy.
The Allied strategy to defeat Japan in the Pacific Ocean was a strategy called island hopping. After the attack by the Japanese on Pearl Harbor on December 7, 1941, the American military in the Pacific was severely depleted. As a result, the Japanese were able to capture much of the central and much of the western Pacific Ocean area. Once we were able to rebuild our military, which was done much faster than most people expected, we were able to counter these Japanese attacks.
Two very critical battles in the Pacific Ocean were the Battle of Guadalcanal and the Battle of Midway Island. At Guadalcanal, the Japanese were hoping to position themselves so they would have a direct path to Australia and to New Zealand, which Japan hoped to capture. At Midway Island, the Japanese were hoping to secure that island so it could attack and capture Hawaii. In both instances, the Japanese were defeated. Japan lost several of its aircraft carriers at the Battle of Midway Island. As a result of the Japanese defeats at Guadalcanal and at Midway Island, Japan would not go on the offensive again during the war. Japan would now be in a retreating mode.
Once we won these battles, we could then begin to implement our strategy of island hopping. We would slowly retake islands in the Pacific that Japan had captured, often with a very high cost in terms of loss of life and equipment, until we got close enough to Japan to consider either continual bombing of Japan and/or an invasion of the Japanese islands. Several key battles occurred with this island hopping strategy. Examples of some these battles included those at Tarawa, Guam, the Philippines, Iwo Jima, and Okinawa. As a result of this successful strategy, we were now in a position to take the final steps to defeat Japan in World War II.
The Allies basic strategy was one of "island hopping," that is, to take back one island at a time from Japanese occupation. A bit of luck was involved, as the American military had broken the Japanese Code, and knew Japanese war plans ahead of time. They were able to intercept the Japanese fleet at the Battle of Coral Sea and again the Battle of Midway Island, and destroy large portions of the fleet. Since Japan did not have the ability to replace lost ships, each ship lost was one less in its navy.
The island hopping strategy was necessary because of the determined fighting of individual Japanese soldiers for whom surrender was dishonorable and unthinkable. It was necessary to destroy all resistance in order to take the island. Eventually, the U.S. was faced with the decision of an invasion of the Japanese mainland islands, or use the Atomic Bomb. Strong factors argued for and against each; however the ultimate decision by President Truman was to use the bomb on Hiroshima and later Nagasaki. This was the final effort that brought about Japanese surrender and the end of the war.