To understand reincarnation and rebirth you need to understand consciousness and what it is that is being reborn. This is actually very difficult to do, because even though we all know we have a mind, we really have a very limited understanding about how it actually works.
Let's use the analogy of a river.
When you stand at a river's edge, the only part of the river that you really experience is, well, this part. Right now, right here. You can look up the river a ways and even down river for a little bit, but really the only river you really 'know' is this segment.
Actually this tiny portion of the river contains a lot of information in it.
Let's scoop up a sample of that water, what is in it? We have a variety of thoughts, sights, sounds, feelings, sensations, smells and tastes. All water bubbles. These come and go in an endless variety. Wherever you are on the river, you will find water bubbles.
What else is there? Oh, here is a preference! That is strange, I wonder where it can from. When you find something, it is possible to trace it upstream to some source. Let's say it is a preference for dark chocolate, what was it in your past that created this preference? Some great experience, maybe a strong dislike of white chocolate led you on a chocolate tasting frenzy and you found a delicious morsel of dark chocolate that to this very day has you searching in local shops for more.
What else? A memory. Let's say it is a face. Where did I meet you, trace and trace and trace and, Yes! I met you at that one event with my great uncle.
What else? Here is a belief. That's weird, where did that come from? Is it cultural, your family upbringing, religious or political. Must have a source, let's investigate.
There must be something else here. Oh, wait. Here is kindness. And love. And humility. And fear. Damn, where did those come from? Where does my sexual orientation come from, my unflagging interest in learning, my desire to build meaningful connections? Honestly, I don't really know. I mean I can trace a lot of that back upstream through my life and find certain markers to indicate their presence, but there isn't always a clear source.
So, the question remains, why don't I remember my past life?
Well, what did you do on June 3, 2014. No cheating. No looking at your calendar to check what your schedule was that day, just tell me. I bet you cannot. You might be able to reconstruct that date based on a nearby event or since it was close to Memorial Day you might be able to infer an answer with some calculation, but really you have no idea. No idea what you ate, no idea what you did, no idea if it was a good day or a bad day, no idea at all. Why? Because there is nothing you can hold onto. It is water through your hands.
Maybe that is what we are supposed to get from all of this, that while we can trace back to events and memories in our past, there is nothing to hold onto. The only way to gain clarity on these matters is to develop a calm and pristine mind, then you might be able to pick up on subtle connections that pervade your past, present and future.
So that leaves one other question, what does our future hold?
What are you doing with the water right now? What imprints and traces are you leaving? How are you influencing its quality and its course? What are you doing, right now? This is really the foundation of all the Buddha's teachings on karma and dependent origination. Everything is contained by simply looking at your mind and your actions.
If you want to know your past life, look at your present condition.
If you want to know your future life, look at your present actions.
Of course the river analogy fits perfectly with our linear perception of time and space, past and future. What happens if we use a vast matrix or even space to understand the mind? Think about it.