The fragmented city-states of Khitai bicker like crows picking at a corpse, each maintaining the fiction that it (and it alone) represents the fallen Khari empire. Periodically, a powerful ruler rises and unites some of the city-states, and the long-imagined Middle Kingdom of Khitai is (temporarily) established. But the huge distances involved in governing such a kingdom, combined with the demand for independence which burst forth at the time of the original slave-revolt, always bring these empires to collapse.
Khitai extended its hegemony over a vast area of the Far East -- from the northern taiga forests to the edge of the Kambujan jungle. Its influence weakened beyond the western satellite kingdom of Kusan, but it claims all the land east of the Mountains of Night.
Khitai has a varied economy. The city-states are centers of manufacturing and commerce. The craftsmen produce sophisticated art-objects. There is ample food from myriad small farms and ranches. Mines produce gold, silver, other metals, and precious stones. Silken textiles, rare drugs, spices, and magical paraphernalia are traded to the West.
The people of Khitai are very ancient -- flourishing during pre-Cataclysmic times. After the Cataclysm, refugee Lemurians entered Khitai and were promptly enslaved. Later, the Lemurians rebelled and overthrew the ancient Khitan civilization before migrating westward.
Khitai is nearly legendary to the average Hyborian, although the more easterly peoples (such as the Turanians and Vendhyans) maintain considerable commerce with the kingdoms of Khitai. Regular caravans now cross the Hyrkanian steppe to reach the kingdom of Kusan and the central city-states. Some traders have even approached Kambuja, hoping to curry the favor of Pra-Eun with their western trinkets. Some Westerners urge caution, however, worried that too much contact with Khitai may bring them to move westward, like their Hyrkanian predecessors.
References: Witch Shall Be Born, Flame Knife, Treasure of Tranicos, Hour of the Dragon, Tower of the Elephant, Curse of the Monolith, Return of Conan, et al.