Not being a big TES lore knower, what do you mean by that?
Basically what Cecilff said. Every object and being (people, animals, trees, stones, grass - even the laws of nature are made up of them) in the world descends/is reincarnated from the Aedra. Not just the Nine Divines, mind you, at the time of the world's creation there were countless amounts of them. When Lorkhan "tricked" them into creating the world the vast majority of the Aedra were forced to "die" and give their whole beings to the world, and became part of it. Those who became people/living stuff is described in lore as having been "forced to marry and make children to last".
And how does this make everybody technically have the soul of a dragon, you ask? Well, lore-wise, and metaphysically-wise, dragons pretty much == gods/Aedra (so does giants, by the way, but that is a whole different story). And
...Alduin, the leader of the dragons we'll face in Skyrim, is the Nordic name for Akatosh, the (dragon) leader of the gods, also titled "the World-Eater" by the Nords and the one who will destroy destroy/unmake the universe. So, anyway, since dragons==gods, and all people have the souls of gods, everyone technically has the soul of a dragon.
Though I doubt Beth cared about that.
I know the discussion has moved passed this, but on the note of the existence of the previous hero... they become Sheogorath at the end of Shivering Isles
. Wouldn't that be a good explanation as to their absence?
That, and even if he didn't, it's still like 400 years later or something.