The Senkaku Islands are a set of ~5 small islands that no one lives on.
Well after WWII, during the Nixon administartion, the US gave them to Japan. But they are much closer to Taiwan (who also claims them), but the Chicoms also claim them (as they claim everything as theirs).
Their value is that they may have good oil reserves. The Chicoms may also be interested because this would serve as a base to invade the east side of Taiwan.
Being so far from Japan, they could be effectively defended only with the help of Taiwan and the US. Without that help, Japan has to make a decision; how much will she pay for these small islands so far from home?
If China gets away with this, Taiwan now knows she is alone and can expect no help from anyone. That changes the politics tremendously.