What is Senkaku/Diaoyu islands:

Eight uninhabited islands and rocks in question lie in the East China Sea. They have a total area of about 7 sq km and lie northeast of Taiwan
These group of islands are known as the Senkakuislands in Japan and the Diaoyu islands in China.
Both Japan and China claim ownership of these islands.
They matter because they are close to strategically important shipping lanes, offer rich fishing grounds and are thought to contain oil deposits.
Right now, the islands are controlled by Japan.

Senkaku/Diaoyu islands

What is Japan's claim?

After World War II Japan renounced claims to a number of territories and islands including Taiwan in the 1951 Treaty of San Francisco.
But under the treaty the Nansei Shoto islands came under US trusteeship and were then returned to Japan in 1971.
Japan says that Senkaku islands are part of the Nansei Shoto islands and hence they also belong to Japan.
Besides, China raised no objections to the San Francisco deal. but only since the 1970s, when the issue of oil resources in the area emerged, that Chinese and Taiwanese authorities began pressing their claims.

These Islands have been part of its territory since ancient times, serving as important fishing grounds administered by the province of Taiwan.
Taiwan was ceded to Japan in the Treaty of Shimonoseki in 1895, after the Sino-Japanese war.
When Taiwan was returned in the Treaty of San Francisco, China says the islands – as part of it – should also have been returned.

In 2010, Japan seized a Chinese trawler that collided with two coast guard vessels near to the islands, sparking a serious diplomatic row. Small anti-Japanese protests were held in several cities in China. However, in the end, Japan released the entire crew of the trawler – first the 14-member crew and then the captain, several days later.
August 2012: a group of Pro-China activists sailed to the islands from Hong Kong, with seven landing on one island. All 14 on board, including journalists and crew members, have been detained by Japanese authorities.

http://www.bbc.co.uk/news/world-asia-pacific-11341139