What is the theme of Twilight?
There is no question that different people will see different themes in this series, but the ones that strikes me involve the difficulties of the outsider and the attraction of the "other."
Both the vampires and the werewolves struggle mightily to fit into mainstream society and still preserve their qualities, personalities, and "differentness." This is a symbol of the struggle of any person who is different in some way, the struggle to be oneself and still fit in. This struggle is particularly difficult in the teen years, and that might be one aspect that makes the book so appealing to teenage readers.
The attraction of someone who is different, the "other," might also be a theme of the book. You will notice that Bella is not the least bit interested in the "normal" boys around her, but put a vampire or werewolf before her, and she is quite attracted. This quality of otherness is often important in attraction, and creates a tension in many teen lives, too, since there is a powerful incentive from one's friends and family to be with someone who is similar, but an equally strong attraction to someone who is different, to try someone new or forbidden.
There will be many different answers to this because the themes of the work mean so much to so many different people. I would say that one of the most compelling themes of Meyer's work would be the idea of teenage alienation and seeking to find transcendence in a mutable world. Bella is completely separated from her social reality and seeks to find belonging in a setting where this concept is missing. Edward is also separated from his reality, as he is a vampire and fears that he will continue to live a meaningless existence. Both of them find some level of solace in one another in that they both seek to establish transcendence and seek to better grasp what lies beyond their reach. In this apparently tragic condition, their beauty becomes more seductive... or at least something like that.
You should probably ask what are the themes of Twilight. I think a partial answer to the question comes in the area of love. I think that Twilight tries to explore the meaning of love and the expression of love from different angles. Also it tries to explore the theme of how love can bridge gaps and differences. Is it possible? For example, a vampire and a human are in love. Finally, there is a related theme of sacrifice or better yet the relationship between sacrifice and love.
The theme could be immortal life versus the mortal life as well as love. Bella is heads over heels with Edward as soon as she saw him and he saved her and he has a strong love for her too but cannot show it right away since he is a vampire and she is a human. Bella on the other hand wants to turn into a vampire and be with Edward forever but Edward does not want to lose her human self from him.
One of my favorite themes in Twilight would have to be Immortality Vs. Morality. First evidence would be Edwards self conflict about whether he decides to take part in Bella's life and risk making either of their lives complicated with her frail being and his immortality that comes with incapable strength. Also there is also Bella's self conflict where she continues to try to figure out what Edward is and whether she can accept the fact that he may not be living human being.