Edward Cullen is a vampire, and the male focus/love interest of Bella Swan (the narrator) in the series. He is exceptionally beautiful/handsome/hot, and fangirls are obsessed with him because he's the supposedly perfect gentleman boyfriend we'd all love to have.
You'll find it's mainly tweens and teens really obsessing over the series. This book is a romance, written in first person, so I suppose it sets the imagination running. Truly though, I really don't understand the obsession with Edward.
It is a good read if you feel like a light trashy romance sort of story, and you're okay with the plot being not very realistic (especially book 4, geez, that was a shocker), then I'd say yes, it's okay. I read the series mainly because of the hype, but generally found it alright as I didn't read too deeply into the plot and making-sense bit.
Borrow it from a library or friend though, and see how you go. I don't think it's worth buying the series, unless you get hooked.