To clarify, while I'm sure it is true that there are a couple of Buddhist folks who claim to believe in reincarnation, it is not a Buddhist belief. Buddhists, like myself, believe in rebirth. The difference is that with reincarnation, it is the ego state that is reborn. In rebirth, the ego state is destroyed at death.

I have often heard people try to make sense out of Buddhist teachings when they come from a culture that is not heavily influenced by Buddhism, by saying that it is the soul that is reborn - but there's no concept of a soul in Buddhism either. In trying to explain the concept to non-Buddhists, I tend to use the phrase 'true self' as opposed to 'ego self'. The phrase is not Buddhist sanctioned but it gets as close to the Buddhist truth as most people care to know.