If there is no soul, what is it that is reborn, one might ask. Well, there is nothing to be reborn. When life ceases the kammic energy re-materializes itself in another form. Here showing itself as a tiny gnat or worm, there making its presence known in the dazzling magnificence of a Deva or an Archangel's existence. When one mode of its manifestation ceases it merely passes on, and where suitable circumstances offer, reveals itself afresh in another name or form.
Birth is the arising of the psycho-physical phenomena.
Death is merely the temporary end of a temporary phenomenon. Just as the arising of a physical state is conditioned by a preceding state as its cause, so the appearance of psycho-physical phenomena is conditioned by cause anterior to its birth. Buddhism does not totally deny the existence of a personality in an empirical sense. It only attempts to show that it does not exist in an ultimate sense. The Buddhist philosophical term for an individual is santana, i.e., a flux or a continuity.