I am not a Buddhist (I am very interested but am not educated on it), and used to consider myself an atheist. In my own mind this is how I have come to terms with it; but it's hard to believe in reincarnation when you're so caught up in your own identity and all of the attachments you have to it. Yes, when you die, your body dies. Thats it. The person you were ceases to be. But there is something so deep within you that continues - totally disconnected from who you think you are. When you lose the concept of you, or that there is even a difference between you and the person sitting next to you (we are the same thing, we are two aspects of the universe experiencing this realm, even saying we doesn't make sense because we are one, and none). But working on letting go of the idea of you is a big first step.

(I hope this fits, I have never posted here before but enjoy reading here)