The collapse of the Han dynasty was followed by nearly four centuries of rule by warlords. The age of civil wars and disunity began with the era of the Three Kingdoms (Wei, Shu, and Wu, which had overlapping reigns during the period A.D. 220-80).
In later times, fiction and drama greatly romanticized the reputed chivalry of this period. Unity was restored briefly in the early years of the Jin dynasty (A.D. 265-420), but the Jin could not long contain the invasions of the nomadic peoples. In A.D. 317 the Jin court was forced to flee from Luoyang and reestablished itself at Nanjing to the south.
The transfer of the capital coincided with China's political fragmentation into a succession of dynasties that was to last from A.D. 304 to 589. During this period the process of sinicization accelerated among the non-Chinese arrivals in the north and among the aboriginal tribesmen in the south. This process was also accompanied by the increasing popularity of Buddhism (introduced into China in the first century A.D.) in both north and south China.
Despite the political disunity of the times, there were notable technological advances. The invention of gunpowder (at that time for use only in fireworks) and the wheelbarrow is believed to date from the sixth or seventh century. Advances in medicine, astronomy, and cartography are also noted by historians.
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.