Smaug was one of the fire-drakes (the mightiest kind of the Dragons and able to breathe fire). I'm not sure where he really came from but I think he's one of the Dragons who was able to survive and escape in the War of Wrath back at the First Age, then he lived in the Lonely Mountain in the the Third Age (destroying the Dwarf Kingdom there and killing several people). I'm not so sure though why he likes treasures very much and I don't think there's a reason given why he had that weak spot. Maybe at the War of Wrath (assuming that he really was there) he was wounded and his scale didn't really managed to cover it up.
According to the books:
ALl the dragons had weak bellies, yes even Glaurung.
The whole belly.
Smaug laid on the goad and gems and they became embedded in his skin, so that even from below he was almost impregnable, apart from an area under the armpit where no jewels embedded themselves.
Presumably they would have chaffed. 😉