Japan occupied the islands shortly after it invaded Taiwan before WWII. After Japan was defeated, it renounced theclaims to the territories it occupied, including Taiway. But Senkaku/Diaoyu lslands were missed from that list because the U.S. had taken possession of it, who used the islands for bombing practice. Since the U.S. says it's not an imperial power and does not take other countries land, it gave the islands back - to Japan - in 1971. But since the islands was originally the result of an illegal occupation of Japan against China, both China and Taiwan claim sovereignty over the islands.
Anyway, that's all historical. The present significance of those unoccupied islands are their proximity to Taiwan and her shipping lanes, the fishing rights, and potential gas/oil field around the islands. The dispute erupted as soon as the U.S. made the move in 1972. But if you ask who is the most at fault, I'd say it's the U.S. Here is why.
Back in 1972, when the dispute originally started, the Chinese position was basically like this: "Look, WWII is bad and invasion of China is bad. But it's over. Let bygone be bygone. Since the islands are important to all of us, why don't we set the issue of Sovereignty aside and start with joint development? Peace and prosperity for all!"
If we had gone that way in the 1970's, there would have been no conflict, and there would have been fish and potential gas and oil exploration for all three parties, and it would have improved the relationships of all three parties involved. But the U.S. came down hard on the Japanese side, knowing that it would irritate China and Taiwan is too reliance on the U.S. to do anything. The U.S. basically told Japan that "do whatever you want and we'll cover your back". So now, instead of a great opportunity for the three neighbors to cooperate and build partnerships, this issue has become a "frozen conflict" in Asia. Sounds familiar with some other current conflicts in the world?
As far as a "frozen conflict" goes, this issue is not that important to any of the three parties directly involved - Japanese fishing fleets roam all over the 5 oceans; China has open-door access to Russia's vast gas and oil fields; and Taiwan would have secure shipping lanes no matter to whom those islands belong. It's just this little rock to keep the neighbors apart, when the annual trading volume between the three parties are already magnitudes more than any conceivable value from these little unoccupied islands. Nobody wants to jeopardize its existing relationship over these islands, but nobody wants to back down either. This is how it stands today.