Reincarnation means there is a soul that goes out of your body and enters another body. That is a very popular, very wrong notion of continuation in Buddhism. If you think that there is a soul, a self, that inhabits a body, and that goes out when the body disintegrates and takes another form, that is not Buddhism.

When you look into a person, you see five skandhas, or elements: form, feelings, perceptions, mental formations, and consciousness. There is no soul, no self, outside of these five, so when the five elements go to dissolution, the karma, the actions, that you have performed in your lifetime is your continuation. What you have done and thought is still there as energy. You don’t need a soul, or a self, in order to continue.

It’s like a cloud. Even when the cloud is not there, it continues always as snow or rain. The cloud does not need to have a soul in order to continue. There’s no beginning and no end. You don’t need to wait until the total dissolution of this body to continue — you continue in every moment.

-- Thich Nhat Hanh