On the book Twilight, the apple, it stands for the forbidden fruit, like in The Bible.
The cover of New Moon has no particular meaning, as Stephenie Meyer had no part in choosing its design.
On the cover of Eclipse, the torn ribbon. It stands for Bella's love. The side of the ribbon each stand for Jacob and Edward, and how they are both pulling her apart, with them both in love with her, and she them.
On the cover of Breaking Dawn, the chess Queen and Pawn. It shows how Bella went from one of the weakest players in the game (the pawn) to the strongest (the Queen).