The bhavacakra (Sanskrit: भवचक्र "wheel of existence"; sometimes also written bhavachakra, since,च, a Sanskrit 'c', is always pronounced as an English 'ch') is a common piece of Buddhist didactic art, particularly popular in Tibet, but also used in China. You've probably seen one before, even if you didn't know the technical name for it; it's the wheel with figures painted in rings and wedges inscribed in it, clutched by a big three-eyed demon, or occasionally a skeleton, with a figure (of a Buddha) pointing at the moon, or a copy of a sutra, outside and above the whole deal.
The oldest known complete bhavacakra images are from Tibet and date from the late 18th century. Fragments of a fresco of a bhavacakra that was painted in the 5th century CE have been found at the Indian monastery of Ajanta. Written compilations of Buddhist monastic regulations, also from the 5th century, though compilations of earlier, orally maintained rules, also mention the bhavacakra, saying that one should be painted at the portico of every monastery, with a monk stationed by it to explain it to visitors. Mahayana and vajrayana Buddhist tradition has it that the first bhavacakra was produced by the Gautama Buddha (who lived in the 5th century BCE) himself, drawn in the sand as a gift for a king who showed him hospitality, but there's no documentary evidence to prove this, nor could there be, really.
This presents two obvious problems in the scholarship of the history of the bhavacakra. First, the date of their first production can't be pinned down to any range smaller than a thousand years. Second, there's another gap, of about 1500 years this time, between the first known bhavacakra image and the next, between which no real information about them can be found. It's safe to say that they were introduced to China from Tibet, but when and how is not known, nor, for that matter, is when they made the leap from India to Tibet. The demon clutching the wheel is almost certainly a later Tibetan interpolation, and the image of the Buddha at the top can date to no earlier than the turn of the Common Era, as the Buddha was never depicted anthropomorphically before then, but neither of these are essential elements of the composition. So, in short, a lot less is known about the history of the bhavacakra than isn't.
As to the image itself, it's a very sophisticated and compact summation of the Buddhist ideas of epistemology, cosmology and psychology. The wheel represents the entire cycle of existence, and the processes that Buddhists believe keep us trapped in it (note: I'm not a Buddhist, but from here on I'm going to present the Buddhist worldview as factual, just because it's tiresome for me to type, and you to read, things like "that Buddhists believe", over and over again). In the very middle, at the hub of the wheel, are three animals, a rooster, a snake and a pig, usually painted as either eating each other's tails, or with both the snake and the rooster eating the pig's tail. The animals represent the Three Poisons, the three negative ideas that keep us trapped in the cycle of existence and reincarnation. The pig is ignorance, which is the root cause of the other two, the rooster is desire, and the snake is hatred. They are at the hub of the wheel, and the rest of it radiates out from them, because they are the root factors that cause the entire process of being trapped with the cycle of samsara.
Surrounding the hub is a ring, broken into two semicircular sections, one black and one white. Inside the ring are small human figures, looking upwards in the white section, and downwards in the black. These represent various possible actions, good in the white section and bad in the black, that cause more karma to be attached to a being, and cause it to move to a better or worse place in the cycle of existence.
Outside this, and taking up most of the space of the image, are images of the six realms, or planes of existence that it is possible to be born into, depicted in pie slice shaped wedges. Most often, these are shown as six realms, with the three on the top half being relatively good, and those on the bottom half relatively bad. At the top is that of the devas, often translated as gods, who live long lives of peace and luxury, never wanting for anything, though they are eventually cursed to grow old and die as everything else, and can't achieve enlightenment, because their lives are too easy for them to understand the dharma. At the top-right is the plane of the asuras, sometimes translated as demigods, Titans, or not-gods, who are also supernaturally powerful and near-immortal, but are exploited by the devas, and spend their entire existences contesting with them, fruitlessly. At the top-left is the plane of humans, who live lives of hunger, turmoil and want, but are in the only realm in which the conditions are right to achieve nirvana.
At the bottom-left of the wheel is the plane of the animals, who spend their entire existences preying on each other, and being exploited by the higher realms. At the bottom-right is the plane of the hungry ghosts, who are cursed to wander the earth, always feeling hunger and thirst, but with their throats too narrow to actually take in any sustenance. At the very bottom is the Buddhist hell, where beings that have committed extreme misdeeds are sent for a period of time to be punished, and it is sometimes divided, by a horizontal line in the image, into the hot hell and the cold hell. A popular variation on this design has five wedges instead of six, with the realm of the devas and the asuras combined into one, and thus with only two wedges on the top, and the position of the animals and hungry ghosts sometimes reversed on the bottom half.
Surrounding these wedges is another ring, this one divided into twelve sections, each with a small figure or icon in it. This is a graphic depiction of the psychological process of interdependent origination, the twelve step process of delusion that keeps our minds fixed within the veil of maya, and thus traps us in the entire process of samsara, which is why the ring is shown as containing the entire image, as it is the chain that keeps the whole process ongoing.
The demon or skeleton that is shown holding and consuming the whole device is a symbol of the impermanence of the whole cycle, everything is constantly changing, being consumed and reconstituted in a new way. The image of the Buddha, above the demon's right shoulder, stands outside the whole process, to show his liberation from it. He gestures at the moon or a copy of a sutra, symbolically showing the way to enlightenment; the moon is a symbol for nirvana, and the sutra is a concrete step on the path towards it.
If you'd like to see an actual copy of a bhavacakra, a decent black-and-white copy of one, one of the five-wedged versions, is online at http://www.horizonscreenprint.com/imgdesc/flags/bhavachakra_desc_flag.htm