China is upset with the United States because the USS McCampbell conducted a "freedom of navigation" operation near the Paracel Islands in the South China Sea, coming within 12 miles of the chain. These operations are meant to establish as international waters areas claimed by other countries in contravention of the UN Law of the Sea (LOS) Convention. By sailing through disputed waters, the U.S. Navy challenges the other country's territorial claims; it is for this reason that China was angered.
The Paracel Islands are claimed by China, Taiwan, and Vietnam. China, however, has built outposts there and also reclaimed land by building artificial islands and building up reefs above the waterline. In fact, China has done this throughout the South China sea in an attempt to press its claims to most of the area, despite the fact that its territorial ambitions extend far beyond its mainland borders, infringe upon international waters, and come close to the shores of other countries in the area.
The South China Sea is immensely important due to its sea lanes and associated shipping traffic, as well as a large amount of oil and natural gas reserves. China claims most of the area as its own, in dispute with a number of other countries, including Vietnam, Indonesia, Malaysia, the Philippines, Taiwan, and Brunei. In addition, the United States and other countries have an interest in maintaining the Sea as international waters. Japan, France, and the UK are among other nations who conduct freedom of navigation exercises in the area.
China's behavior in the Sea is almost universally condemned by the international community, although beyond conducting a few naval exercises in the area, no one has done much to counter China's actions. China has lost in past arbitration and ignored treaties, continuing to expand its military and commercial presence in the Sea (photos available here).
A map illustrating the competing claims of China and its neighbors is available here.
(Main Image: USS McCampbell, by U.S. Navy, Public Domain, https://commons.wikimedia.org/w/index.php?curid=8224174 )