The most far out idea of Buddhism is reincarnation. It is difficult to imagine that we live more than one life. What is it that survives our death and comes back in another body? Zen makes the idea of reincarnation simple. Your past life is yesterday. Your next life begins now. We are reincarnated in every moment. As we get older, it gets harder and harder to remember our past lives. Who were we when we were two years old? Who were we when we were 12? We were certainly something different than we are today. Who will we be tomorrow?
When you look at reincarnation as a constant process rather than a cosmic passage from death to birth, then you can see the importance of Karma. If you are nice to people in this life, in your next life (tomorrow), people will love you. If you are nasty to people in this life, you will be isolated in your next life. What we do now impacts our future lives. It is important that we practice kindness and compassion so that we will be happy in our next life (starting now).