What does the cover have to do with Breaking Dawn?

Answer 1

The Chess game represents the ending of the book, that the Volturi were dealt with logically, instead of bloodshed, because chess is an entirely mental game. The chess pieces represent Bella: The red pawn is her when she's human, as she was the weakest character, and the pawn is the lesser of all the chess pieces. The white queen is her when she's a vampire, when she gains the ability to shield others, resulting in the Volturi's retreat - making her a very powerful character, hence the portrayal of a queen chess piece.