I won it from that dwarf and it says it's a quest item but I don't know what it's for. Any ideas?

This is a guess as i solved the quest by answering his questions correctly, but I think if you get it and the beaver cap you can use it to trick the Dun Banner wraith without having to answer his questions, he'll just see you as one of the boys and hand you the banner. Speculation, as i said. I got the beaver cap after I had finished that part, so can't say for sure.

*******SPOILER*******

If you have it, the Dun Banner wraith will allow you to make one mistake during the questioning about the Dun Banner history. That happened to me.

Umm, he allowed me one mistake when I didn't have the banner iirc. Had the cap though...