The Twilight covers are all supposed to represent something, and I know the apple represents temptation, but what do the New Moon, Eclipse, and Breaking Dawn covers mean?
The New Moon cover doesn't represent anything in particular, as it wasn't chosen by Stephenie Meyer.
The Eclipse cover (ie. the ribbon) represents the emotional ties that keep Bella human(ie.Charlie, Renee, Jacob etc.)from her new life as a vampire.
On the Breaking Dawn cover, the red chess piece represents the human Bella and the white chess piece represents Bella after her transformation into a vampire.
I think this is what the covers mean, hope that it answers your question.
Yes, the apple on Twilight is resisting temptation.
New Moon doesn't mean anything in particular as Stephenie Meyer didn't choose it
The ribbon on Eclipse represents Bella's heart as she is forced to choose between Edward and Jacob (Team Edward! XD)
Breaking Dawn- the pawn is supposed to represent her as the small insignifcant human at the start of Twilight and the Queen is her as the strongest vampire at the end of breaking dawn.