Extend consciousness

"The idea that there is a connection between this life and the events of both our previous existence and our future existence, follows from the Buddhist understanding of the natural law of cause and effect." -The Tibetan Book of the Dead (xv)

If we were to believe in some level of continuity of consciousness, this would extend our ability to understand our existence in relation to the universe.  We would also grasp a sense of real and prolonged consequences from our own actions, in terms of our own lives, the lives of people around us and the environment.  What we did yesterday would then be understood to impact today as well as tomorrow.  What we experienced in previous lives would then help to explain where we are now and how we think.  Although certain levels of sensory perception depend on the functioning physical body, the question that remains is what kind of underlying essence could affect awareness after death and how we could retain knowledge of past experiences?