Twilight
Stephenie Meyer has stated that the apple on the cover represents the forbidden fruit from the book of Genesis. It symbolizes Bella and Edward's love, which is forbidden, similar to the fruit of the Tree of knowledge of Good and Evil, as is implied by the quote from Genesis 2:17 that opens the book. It also represents choice. :D

New Moon
The flower on the cover of New Moon is a red and white Parrot tulip. Stephenie Meyer has stated that the flower has no significance to the story, as she had no part in choosing its design. The title refers to the darkest phase of the lunar circle, indicating that New Moon is about the darkest period of Bella's life.

Eclipse
The broken ribbon represents choice, as in the book Bella must choose between her love for Edward Cullen, her vampire boyfriend, and her friendship/love with Jacob Black. Meyer also stated that the ribbon represents the idea that Bella can't break away completely from her human life.

Breaking Dawn
Breaking Dawn's cover is a metaphor for Bella's progression throughout the entire saga. She began as the weakest (at least physically, when compared to vampires and werewolves) player on the board: the pawn. She ended as the strongest: the queen. In the end, it's Bella that brings about the win for the Cullens.

Twilight
Stephenie Meyer has stated that the apple on the cover represents the forbidden fruit from the book of Genesis. It symbolizes Bella and Edward's love, which is forbidden, similar to the fruit of the Tree of knowledge of Good and Evil, as is implied by the quote from Genesis 2:17 that opens the book. It also represents choice. :D

New Moon
The flower on the cover of New Moon is a red and white Parrot tulip. Stephenie Meyer has stated that the flower has no significance to the story, as she had no part in choosing its design. The title refers to the darkest phase of the lunar circle, indicating that New Moon is about the darkest period of Bella's life.

Eclipse
The broken ribbon represents choice, as in the book Bella must choose between her love for Edward Cullen, her vampire boyfriend, and her friendship/love with Jacob Black. Meyer also stated that the ribbon represents the idea that Bella can't break away completely from her human life.

Breaking Dawn
Breaking Dawn's cover is a metaphor for Bella's progression throughout the entire saga. She began as the weakest (at least physically, when compared to vampires and werewolves) player on the board: the pawn. She ended as the strongest: the queen. In the end, it's Bella that brings about the win for the Cullens.