Former Christian, technically still an ordained priest of the Latter Day Saints.
Currently resides somewhere closer to Buddhist beliefs, and is a firm believer in reincarnation.
Reporting, as much as that matters.
As a believer in reincarnation, what is it you believe reincarnate? our soul, meaning a distinct entity that gets reborn into another human being? what gets carried on through this distinct entity (or in other words, what are the qualities and characteristics of this entity)?
Yes, I believe that there is some form of "soul" that persists between incarnations.
To better explain it: I believe that the "purpose" of life is simply to learn. There are many religions that believe this. In any case, it's not possible, in any sense, to learn all there is to know, or even all that you want to know, within a single lifetime.
So I do believe that there is some form of knowledge or information that resides within the soul, that could possibly be transfered to the present physical body. (Whether you'd realize it happening or not wouldn't really matter)
Obviously, though, you wouldn't remember them, because your ability to learn is skewed when you have prior experience, because you already think you understand how it works, and aren't as open to new ideas, as if you had a blank slate for your memory.
As I imagine it will inevitably be asked where souls come from, the Bhagavad-Gita (One of the many book of Hindu scripture, but it shares a lot of beliefs with Budhisim) does a better job of explaining than I could do, in that it explain that just as God is immortal, and has always existed, with no beginning, so too has every person's soul, always having been.