Well, I used to be a Twilight fan. I have to say, I outgrew it, but I think I can help.
Twilight was the first romantic book I had read, and I think I liked it so much because of that. Edward is described as "the perfect guy", handsome, charming, and completely in love with Bella. Bella was just an average teenage girl, who got thrown into this exciting life filled with vampires and werwolves, and even has a romantic relationship with both. A lot of girls want to imagine that that can happen to them. That you don't have to be special to have something amazing happen to you.
Plus, there's the action and the shirtless guys.