The kirin is a mythical creature often compared to the unicorn of western medieval lore, due to the single horn it bears on its forehead. Unlike the long, spiralling horn of the unicorn, though, the kirin's horn is more often depicted as antler-like, or resembling a dragon's horn, which suits its dragon-like head. It has the body of a deer, but the single-toed hooves of a horse, and a long curving tail like an ox. It is sometimes depicted with wings--though whether it has physical wings or not, the kirin can generally fly.
The kirin depicted in The Twelve Kingdoms (both in the anime and in the light novel series it is based on) match this general description, though their heads are deer-like, giving them an apearance much like the western unicorn. They are beautiful, magical creatures that can run over land or through the air. Once difference, though, is that the kirin of The Twelve Kingdoms can also take human form.
In the novels and anime, kirin have servants called sirei that are taken from among demons--the kirin dominates the demon with its will and then makes a pact with it. This may be based on the idea that of all the creatures that walk on land, the kirin is the leader, as the phoenix leads the creatures of the air and the dragon leads the creatures of the water.
It is said that the kirin is so rare and special that it might appear only once in a thousand years, and that when it does appear, it heralds a significant event or the birth of an important person. The birth of Confucius, for example, was marked by the appearance of a kirin.
In The Twelve Kingdoms the lore of the kirin's rarity manifests as the presence of only twelve kirin (or fewer) in the world--one for each kingdom. A new kirin is born only when an existing one dies. In the world of The Twelve Kingdoms, the kirin is also a herald of important events and people, as it is the kirin's sacred duty and its purpose to choose a new king when an old king dies. Because royalty is essentially immortal, the choosing of a new king is a rare and important event.
Another aspect from ancient myth that is found in The Twelve Kingdoms is that "ki" refers to a male kirin and "rin" refers to a female, so the species as a whole is called "ki-rin." In The Twelve Kingdoms, this is taken a step further, so the name of each kirin is composed of the name of the kingdom it serves, plus "ki" or "rin" depending on the kirin's sex. So the kirin of the Kingdom of Kei is called "Keiki," the kirin of Tai is called "Taiki" and the kirin of Kou is called "Kourin."
The creature is said to be so gentle it treads carefully to avoid injuring even the plants it walks upon and it cannot bear to eat anything living. In The Twelve Kingdoms this gentleness manifests in the kirin becoming weak and ill at the sight or smell of blood. Even the presence of another person who has recently killed or been nearby when killing happened can make the kirin sick.
According to Shigeru Mizuki, even though legends of kirin have been part of Japanese mythology for a long time, the creature itself does not seem to have acclimatized to the islands. Perhaps this is why the kirin of The Twelve Kingdoms can travel to Japan, but only do so when they must--such as when their chosen king is there--and generally remain in the Kingdoms whenever possible.
The Twelve Kingdoms light novels by Fuyumi Ono currently number seven in Japan (several of them were published in two volumes, however), but only the first four have been published in English. They are available in hardcover and softcover from Tokyopop, but volume one is increasingly difficult to find. Due to the apparent unpopularity of light novels among English-speaking readers, it seems unlikely that the rest of the series will see English release.
The Twelve Kingdoms anime was a 45-episode series and got an English-language release in 10 volumes from AnimeWorks that can still be found at some retailers.