Dependent origination, or dependent arising, is a formulation that is central to Buddhist philosophy. It is depicted as a wheel in the Bhavacakra, or Wheel of Life and Death, a popular subject for Buddhist paintings. According to the Divyavadana (Divine Stories), the original illustration was created by the Buddha while teaching the second noble truth to King Rudrayana.
In illustrations of dependent origination, the wheel is held in the grasp of Mara (or Yama), the lord of death. In the center of the wheel the three poisons are depicted — a pig, a snake, and a cock, representing delusion, anger, and greed. The next ring of the wheel shows the realms of existence: heavens, hells, and realms of humans and animals. On the outer edge of the wheel, the cycle of dependent origination is illustrated.
The Wheel of Life and Death is a depiction of the universe where all beings reside, but it is also the universe of each individual as he or she faces samsara. It is a map of the way that rebirth arises, of how human realities arise out of mental states. The cycle of dependent origination represents a human life cycle, but it can also represent cycles within a lifetime, such as the life cycle of an addiction, a relationship, a job, and so forth. The cycle of dependent origination can be brought to an end at any point in the cycle, although ignorance is typically the place to begin.
Rebirth begins with ignorance, and is sparked by one of the three poisons. Ignorance gives rise to volition, which gives rise to consciousness. Consciousness gives rise to a body (name and form), which gives rise to the six senses. The six senses lead to contact, which leads to sensations, which lead to desire. Desire gives rise to clinging, which leads to becoming. Becoming leads to birth, which gives rise to old age and death. Birth in this case is the creation of a set of predispositions that will structure one's volition in the next cycle.
For the western reader who cannot identify with the idea of samsara, dependent origination may be difficult to understand. An example might be helpful. Imagine that in a previous life you were an alcoholic. You've passed away, but the desire for alcohol is still strong within the part of yourself that survives. That part thinks, "If only I were alive again, I could drink." Eventually, from this desire a new life is created, and so the cycle of dependent origination begins again, with ignorance.
The cycle continues. You are unaware that drinking is not going to bring you the happiness you seek. You have been born with the volition to drink, as a result of the karma you have carried from your previous life. When you reach a certain age, you become conscious, and you become aware that you have a body, that you have been reborn. Chances are you have been born into a family of drinkers, since it is the motivating factor in your rebirth. You are around alcohol all the time; you can smell it, you can see it, you can experience it with your senses. As soon as you get the chance, you grab a drink and you drink it (contact). You have the sensation of a having a little buzz. This only makes you desire more drinks. You cling to the idea that drinking will bring you happiness. So you keep drinking, every chance you get. You are on your way to becoming an alcoholic. After awhile, your identity as an alcoholic is solidified — it is (re)born. Being a drinker is now an essential part of who you are. You live the rest of your life as an alcoholic, and then you die. After death, the desire for alcohol remains, and so the cycle begins yet again.
Just as suffering arises from the cycle of dependent origination, salvation can arise from understanding the causes of suffering, or, to put it another way, from eliminating the ignorance that has prevented recognition of the causes. Instead of living a cycle that leads to the rebirth of an identity as an alcoholic, you could develop the identity of an AA member. Or you could become a teetotaler. Or it could be that something else will become the focus of your identity, be it family, a profession, or a skill. Or you might realize that any identity is impermanent, an illusion. There are many ways you could overcome your ignorance and avoid that endless cycle of death and rebirth.
It is not necessary to interpret this cycle in terms of past lives. All humans experience cycles through which their identities are formed. For example, one may go to school and start a profession; one could fall in love and get married; or one might have children and become parents. Any cycle of this kind creates a sense of personal identity, and any negative cycle can be broken. Where problems arise, according to Buddhism, is when one begins to think of these characteristics of one's life as permanent and unchanging, as the whole of one's identity.