Bella’s dreams and hallucinations in New Moon provide insight into Bella’s psyche – they trace her character arc, and the way she moves and grows through her painful breakup. The story starts off with Bella’s dream about her grandmother, who turns out to actually be her:
Me – ancient, creased, and withered… Edward… excruciatingly lovely and forever seventeen. (1.21)
The stages of Bella's pain are connected to her recurring nightmare of running through the forest on desperate search for something that only leads into nothingness (5.17). Her dreams also foreshadow future events that help drive the plot forward – Jacob’s transformation into a werewolf, for instance:
The dream veered off… The wolf stared at intently at me, trying to convey something vital with his intelligent eyes. This black-brown, familiar eyes of Jacob Black. (12.156)
Bella's last dream leaves her with the image of an angel who turns out to be Edward, who’s come back to her (23.1).
Bella’s hallucinations present a projection of her subconscious desires. For details, check out her "Character Analysis."