In the simple form, when we die, at the end of this life, our consciousness and our Kammic makeup, the result of all our good & bad actions, will be reborn in another body. It may be human, if we deserve to be reborn human. It may be in a heaven realm, a hell realm or it could be an animal. It depends on our Kammic makeup, how much goodness we've done. It also depends on our last thought at the moment before dying. This will dictate, what kind of a rebirth we will get. Rebirth then occurs over and over, and it will continue to occur until a person is fully enlightened. When a person is fully enlightened then there will be no more rebirth. That's the basic concept.
Now that's the body rebirth. In our practice we also want to understand the moment-to-moment rebirth. You're being reborn each moment. You're not the same person you were before I read this question. You now have new information. You're not the same person you were before I read any of these questions. You're changing, moment-by-moment, all the time. The person who you were, who walked into the hall, he or she has passed away, gone. You won't find that person on the whole planet. You might find someone who looks very similar to that person, who has ninety-nine point nine percent of the same thoughts, but it won't be exactly the same, because you now have some new thoughts and concepts.
Even science tells us, some of your body is gone, and some of it's brand new. Cells are reborn all the time, and every seven years your entire body is brand new. We can see our body does change over long periods of time. So it's important to look at rebirth as in this life and other lives not only in the long term, but also moment by moment. When you look at it moment by moment, one of the most important things to understand is that who you are now, conditions who you will be reborn. What you do now conditions who you will be when you are reborn. If you're angry right now, chances are you're going to be an angry person in the next minute. If you're loving right now, chances are you're going to be a loving person in the next minute. So that's another way to look at rebirth.