Twilight Cover: Means the "forbidden" fruit like form the Garden of Eva. Like in the bible god told Adam and Eva not to eat the forbidden fruit form the Garden of Eva but they did any way. And because of that they paid the consequence. So on the cover Edward is the "forbidden" fruit and Bella comes and takes a bite out of him.lol.And we all no what happen when you do that there are going to be some major consequence she will have to pay. Just like Adam and Eva.
New Moon Cover: Means the torn, bloody love of Bella's and edward's Relationship.
Eclipse Cover: Mean that Bella is feeling torn between her friendship with Jacob and her relationship with Edward.
Breaking Dawn Cover: The red pawn piece stand for Bella as a human how she is always the weaker player (that why the piece is red because of her being human). And the white queen pawn piece stand for when she is turned into a vampire (that why it is white) it showed us that she will come out on top in the vampire world (that's why she is the queen of the pawn piece on the cover)