This place is an island state off the southern coast of China. To all intents and purposes, it is de facto although NOT de jure independent, is not a member of the UN, and not officially recognised by most countries of the world, although just about everyone trades with them anyway. It is also known as The Republic of China. China claims ownership over the island and views it as an unruly renegade province that is temporarily giving the parent some headaches. As for the Taiwanese, they are split over whether to be fully independent, or just keep quiet about the whole thing and continue making loads of money out of selling high tech goods to the rest of the world. Presently, those that wish this state of affairs to continue are in the majority and don't wish to rock the boat, thank you very much. Which comes as something as a relief to most people, especially the US which is treaty-bound to defend the place in the event of an attack, as the mainland has said any formal declaration of independence means they'll be trying to put lots of boots on the island.
Taiwan was first populated by seafaring tribes of Malayo-Polynesian lineage, but those were crowded out into the island's central mountains when mainland settlers began showing up; they currently account for 2% of the population, the other 98% being Han Chinese. The Westerners took an interest in the island from the 16th century, and it was claimed in turn by the Spanish and the Dutch. In 1661, a Ming loyalist and Triad leader named Zheng Chenggong gathered a pirate fleet and evicted the Dutch. By the end of the 17th century Taiwan had submitted to Qing rule, but it remained a neglected backwater until a French attempt to annex it in the 1880s, which resulted in it being belatedly promoted to full-fledged imperial province. From 1895 to 1945, it was a Japanese colony, and by most accounts a decently-managed one.
Taiwan was the bolt-hole for the fallen Kuomintang Nationalist government of China under Jiang Jieshi who retreated to the island following their defeat in the Chinese Civil War in 1949. They set about brutally suppressing the local people when they arrived. However over the years, the Kuomintang Party's grip loosened and their rule became less oppressive, with the island moving toward full democracy towards the end of the 20th Century. The Japanese period of colonial rule was, in contrast to their rule in over parts of Asia, comparatively benevolent, and they did much to improve and develop the infrastructure of the island. Many older Taiwanese as a consequence tend to look back on that period with a degree of nostalgia, almost certainly the only Chinese who do so. As with other places in Asia, Japanese pop culture is very widespread and popular in Taiwan.
One of the interesting cultural idiosyncrasies of Taiwan is the custom of having pretty girls in very skimpy clothing sell betelnuts to passing motorists from roadside booths. How male Taiwanese drivers manage to keep their eyes on the road with such distracting sights to tempt them remains an unsolved mystery.
A PRC invasion of Taiwan within the next 20 years is something of a FH Cliché.
Taiwan is often cited as an example of successful regional resistance to European colonisation, due to the ejection of the Dutch in the 17th century.
Due to its claim to be the legitimate government of China, Taiwan has perhaps the most outrageously chutzpah-laden land claims in the world (see here: http://strangemaps.files.wordpress.com/2007/12/roc_administrative_and_claims.jpg).
Given that its status is vaguely disputed, it is probably only a matter of time before Sargon annexes it.