Age also is a factor - as there are certain chemicals in our brains which are needed during REM which decline as we get older.

He told me that I had the ability to break through to this other realm. Does anybody have any idea about what this could mean??
Well, DC's say all sorts of strange things. Since they are really reflections of ourselves, it's likely it's simply stating something that you really believe in your subconcious. But, if you want to look deeper into the meaning, I'd give the whole metaphysics/quantum mechanics thing a look, which proposes parallel universes all around us which we can not see.