The Twilight Cover:The Apple is a forbidden fruit, dont ask me why, which symbolizes Edward and Bella's Love.
The New Moon Cover:
The flower represents, relationships dying and growing together with new petals.
The Eclipse Cover:
The ribbon means, one shade is for Edward and the other is for Jacob and the relationships, with Bella are breaking, but she is still holding on to both of them.
The Breaking Dawn Cover:
The pawn represents Bella's human life, weak, and the queen represents Bella's vampire life, strong.