"Read the bo...screw it, I'll give you an answer on this one."
Note that this is not a major theory (it's not one of the "Big Ones") and will mean little to TV viewers, but it's a nice minor theory that has engendered a lot of discussion over the last decade.
Spoiler after the cut:
From the comic book adaptation of The Hedge Knight, art by Mike S. Miller (pencils) and Mike Crowell (inks).
The theory is that Brienne of Tarth is the descendant of Ser Duncan the Tall, the companion of the young Aegon V Targaryen and protagonist of Martin's Tales of Dunk and Egg novellas, recently collected in A Knight of the Seven Kingdoms. This is based on the fact that the shield that Ser Duncan has commissioned in The Hedge Knight somehow ended up in the armoury on Tarth, the Sapphire Isle, when Brienne was younger. She recalls seeing it there in A Feast for Crows. Although there are other ways it could have been there, the most obvious is that Dunk married a daughter of House Tarth and they had a son, who became Lord of Tarth (presumably because the daughter had no brothers). The daughter died at some point, allowing Duncan to later become a member of the Kingsguard, rising to become Lord Commander and meet his ultimate fate on the night of the Great Fire of Summerhall.
George also once said that we'd meet a descendant of Dunk's, and a clue would be found in A Feast for Crows. Brienne's shield is the only thing that really comes to mind.
At BaltiCon, fan Kristen Reed Treado asked, "Will we ever learn how Brienne descends from Dunk?"
GRRM replied, "Eventually. All will be revealed in time."
Other sources have confirmed that George meant that yes, Brienne is descended from Dunk but we won't learn more about the lineage until either later novels or further Dunk & Egg stories clear up the puzzle.
As I said, not one of the critical theories but it's certainly nice to get at least one mystery cleared up.
George also confirmed that he was working on The Winds of Winter and had been writing a Cersei chapter before attending the convention. No new estimate was given as to when the book would be finished.