Temptation - it's a reference to Adam and Eve, where the apple is used as a symbol of temptation (Eve gives in to temptation and takes a bite of the apple and Adam follows). Similarly although Bella and Edward shouldn't be together, one being a human and the other being a vampire, they can't resist each other and give in to temptation. However, Edward never goes so far as to actually bite into Bella's skin and suck her blood for pleasure.
i think the apple stands for forbidden fruit. bella being the forbidden fruit and edward wanting her but not being able to indulge in her because of the restrictions of being a vampire.