Good question. It was one of the questions I had to work myself through on my journey as well.
Most people think of the soul and reincarnation like this - My name is Mark and my souls name is also Mark, and it looks just like I did when I was 20, and its separate from everyone else's soul, and when my body dies this soul will be placed into a new body.
This way of thinking is an attempt to preserve the ego, even beyond physical death. Don't feel discouraged if that is what you are doing, the ego is very powerful and will do everything it can to preserve itself.
The way I think of it is like this - This light is not my own. We all share the same eternal soul, and all other beings I will ever witness in my life are other incarnations of myself existing simultaneously. In that way, this one great soul reincarnates itself. And yet, you are that.