I don't want to go into detail of my experiences which have lead mem to this conclusion, but let me try to explain how I see it, but you'll need this picture to understand.

In each world, you are endowed with a body, and a soul. And you start at some position on the web (the universe) as a droplet of water. When water flows down, and the droplets break off into other ones, they do not lose their content- they are the same water from before they broke off into another drop- and so they continue down the web to come together in the middle again. So, we start in one universe, things branch off, new worlds are formed by alternate choices, and our soul is in those other worlds, however, we are only conscious of one world per droplet. But we are not separate from our other droplets; they are fully and wholly us, not "part" of us, but us. The water, despite separating, is a complete full droplet. And our droplets will come back together when we die, and we'll remember all the other worlds we lived in. Some people are conscious enough to be aware of these other worlds via various means, which you sound like you might be to some degree.

If you have any questions, do ask! :) Also, I think if you jump realities, the "droplet" you switched with, for lack of better terms, switches with your droplet, but I may be wrong on that one. I've never switched, only seen.