I can see what the appeal is, although it is hard to explain to someone who isn't willing to give it a chance.
My boyfriend took me to see the first movie and I was convinced I would detest it (I thought the trailer was ridiculous). But I was hooked after having watched it. I then read all the books and enjoyed them. I have since seen the other movies and have the first two on DVD.
I don't think Kristen Stewart or Robert Patterson deliver superb performances. The books are not incredibly well written. That doesn't matter though.
It is simply the premise which holRAB the appeal - she is a nice, ordinary girl who falls in love with someone who she believes is worth 100 times more than her - and, he loves her back.
You can enjoy the thrill of those feelings back when you were a teen and have fallen in love for the first time (or can help your fantasies if you are young enough without having experienced it just yet). The love, the affection, the sexual tension, having this one person mean the world to you. Having this amazing secret of him being a vampire, you shouldn't be together but nothing can stop you.
Then throw another guy in the mix (Jacob), totally opposite to Edward and also mad about you. Add in some drama of people trying to kill you, your lover protecting you and college/homework being the least of your worries. It takes you from the mundaneness that is life and lets you escape into a fairytale world of craziness, hotness, fear and fun.
It's great fun. I'm looking forward to the next movie. I think that the only one who has demonstrated much acting talent is Taylor Launter who plays Jacob.