The immortal vampire (as opposed to the mortal ones that just consume time emotional energy and disappointment in the sack) is a hero in the Buffy universe. Defender of the weak, friend to the brave and possessor of the bluest balls of all mankind.
Angel was born 250 years ago in a section of Ireland where the people sound remarkably American. I believe it was Galway. His birth name was Liam. However his name and his life changed one night when he went home with Darla. In what was either the best or the worst decision of his life he allowed his penis to do the walking and ended up one of the undead. Darla, for her part, just thought he was sexy. I think we can all see her point.
He and Darla (later joined by Spike and Drusilla) went of a rampage through Europe, consuming whole nunneries, towns, inns and random stagecoaches (see ineffective government agency's of the Buffyverse) until one day he ate the wrong lady.
In what would become a theme for his life he paid dearly for the indiscretion when her father, it turned out, happened to be a magical ninja gypsy warrior and cursed Angel with his soul. (Oh, I didn't mention he lost it when he became a vampire? Yeah, he totally did. It happens to all vampires. It looks like most people have this problem killing and eating people for food or sport if they have a soul. Without the soul it's easy peasy cover girl. With notable historic exceptions like Hitler, Stalin, Ho Chi Min, Jeffery Dahmer, Pol Pot and that guy in Uganda.) The curse works thusly. See, before when he killed, tortured, mutilated, raped and horribly dismembered people it was all in good fun. After, he is wracked with guilt for the rest of his immortal life, cursed forever with the memories of what he has done and the knowledge that he will never be redeemed no matter what he does. He also can't have sex.
Yes, I know the curse says a moment of "true happiness," will take his soul away but that is apparently TV speak for "getting some hot and sexy lovin' from the woman I adore." Yes friends, when Angel comes there he goes.
Angel then spent a unbelievable period of time feeling sorry for himself, eating rats and working for the US Government (see ineffective government agency's of the Buffyverse) until one day he met Buffy Summers. She was everything he looked for in a woman. Strong, sassy, able to round house a bitch and he fell in love. Buffy saw in him everything she had been looking for as well, brooding, strong, able to round house a bastard. As people in love are wont to do they soon did the hot and sexy. It was at that point that the incredibly specific nature of the curse revealed itself and Angel lost his soul. Becoming for all the world to adore, an irredeemable prick.
He got better (as popular characters are wont to do) died, came back to life and decided to leave Sunnydale for obvious reasons. I mean, no one wants Willow sitting outside their bedroom ready to reensoul a lad every time he decides to had a romantic evening. That would be just stupid. He went on to have his own TV show, fight for good, fight for evil, love, lost, it was better than Cats.
There comes a point in every woman's life where the idea of sex becomes intensely compelling. Yet at the same time most women are smart enough to know it is probably an intensely bad idea. Mostly because at this time they aren't women they're girls, maybe 12 years old. So, the idea of a man who wants you with intensity of a thousand suns but who can't have you because of circumstances beyond both your control has some appeal. You don't even have to say no. He does all the heavy lifting and your job is to simply be adored (see that guy from Twilight, Boy Bands, promise rings). Angel is the embodiment of that desire.
He also embodies that fear women have when they're younger that if you have sex the guy you love will turn on you because you're a dirty, dirty whore. With time and experience everyone learns that sex partners, both male and female, will love you're dirty, dirty whoreness. When you're young, lets face it, what the fuck do you know?
For more on fictional expressions of female sexuality see Spike (as that guy you have hot amazingness with whom you will never give your actual address), 007 (as that guy you don't have to worry about sticking around), every character Michael Cera has ever played (as that guy who starts crying right in the middle who forces you to make the decision, "do I comfort him or go home and watch Lost?") and finally Colin Firth (as that guy who does not in fact exist).