The Buddhist Concept of Death and Rebirth:

The concept of rebirth is unfamiliar to most Western people. Its philosophical and traditional foundation is found in India, where the theory of transmigration of souls had presumably existed long before it was written down in the Upanishads around 300 BC.

The Buddhist concept is subtly different from the classical Indian understanding, because it denies the existence of a self or a soul. In Buddhism, the idea of self is merely an illusion. Man wrongly identifies perception, consciousness, mind and body with what he calls self. In reality, there is no abiding entity that could be identified with a self, because the states of perception, consciousness, and mind and body constantly change.

The body is mortal and when it dies, all mental activities cease. That is why there is no soul. The idea of soul is simply an extension of the self; in fact it is an immortal version of the self that supposedly survives physical death. Buddhism denies the existence of such an entity. Instead, what we call self is just a stream of consciousness that draws identity from concepts and memories, all of which are impermanent.

The idea of an abiding self is deceptive, because it is derived from unenlightened reasoning. The word self simply provides a reference frame for the mind-body phenomena of sentient beings. We usually identify it with our body and the stream of consciousness that is sustained by sense perceptions and thoughts. In reality, what we call self is neither abiding nor detached from the rest of the world and other beings. Buddhists call this the "neither self nor non-self".

http://www.thebigview.com/buddhism/karma.html