Three Kingdoms (220 - 265) Dynasties of the North and South (317 - 589)
While there was a great deal of political activity occurring during this period, most of it, consisting as it was of various wars between different kingdoms (one of the great novels of China, The Romance of the Three Kingdoms, is about this period), was not terribly important to the later development of China. Perhaps its greatest accomplishment was to reinforce in Chinese thought the importance of having "one Emperor over China, like one sun in the sky."
Socially, though, there were two important developments. The first was that the ethnic Han Chinese kept on moving south, while 'barbarians' moved into the north and assimilated themselves into Chinese society. The second development was Buddhism, which had had its start in India sometime in the 6th century BC, when the Buddha probably lived. It was introduced into China around the middle of the first century AD (probably about the same time that the early Christians were writing the Gospels), but really didn't catch on until the fall of the Han dynasty.
Buddhism competed strongly with Confucianism, and for a long time, pretty much eclipsed it as a major cultural force. For various reasons -- some political, some social -- it spread very quickly throughout China. It also changed somewhat from the Indian original, which, as far as I know, is not practiced anymore anywhere in the world. From China, Buddhism would spread into Tibet, Southeast Asia, Korea, and Japan.
Buddhism also merged somewhat with Daoism, particularly as a popular religion; and while the process may be compared to Christianity's appropriation of indigenous European beliefs and traditions, Daoism maintained its own identity and was not subsumed into popular Buddhism.