Presumably he fought "the serpents of the north" and got his scars from that battle.

Thats a weird scene.

It's never mentioned in the books to my knowledge, so I think it's something the film makers just decided to do. As Jpcc86 says he was involved in some battles prior to the third age and the events of the hobbits, so it's probably linked to that.

If I remember correctly the dialog during that time offers the best proof. Thorem and he were talking about the facing the dragon. And he mentioned, I don't remember the wording, but it seems he faced off with something about as powerful, which kicked his butt. And yeah I'm guessing this is drawn from the "unfinished/originally unpublished" short stories that Tolken's estate had published after his death, and Peter Jackson used these  to pad the story to make one book into three films. (So the scene was mostly a dick measuring contest.)