It's sometimes hard to get people to take you seriously when you're claiming that a show with a title like "Buffy the Vampire Slayer" is not just a guilty pleasure, but is actually really good. So I'm going to take another stab at explaining why it's so much fun to watch, and why you should give it a serious chance and watch a few episodes if you've never had a chance.
Perhaps the first and most obvious thing to mention is the writing. The dialogue is actually intelligently written. The smarter/more educated characters talk over the heads of some of the others, and not infrequently over the heads of some of the putative target demographic. Just as Bullwinkle and Warener Brothers Cartoons were written for adults as much as for children, Buffy is written from a perspective and background knowledge that exceeds the putative "typical teen." I'm not trying to slam teens with this comment about the "typical teen", just to recognize that the teen audience as imagined by the networks is not too bright. (As Buffy said about Faith: "She's not playing with a full deck. Actually, I think she has a 2"). Personally I think that the network executives' idea of teenagers is as basically inaccurate and hostile as the recently-forged "gun-toting, mass-murdering teenager" stereotype.
So the dialogue is funny, but the plots generally have serious elements that are very real: duty, betrayal, friendship, career choice, getting into an accident in your mother's car, finding a cream rinse that is both creamy and rinsey, staying within one's shoe budget. In short, it reflects the blend of humor, angst, trivia and horror of day to day life. OK, it's a bit heavier on angst and horror than even my life as a teenager, but the most horrible things are still the internal ones, like the way that some boundaries, once crossed, are never fully recrossed. Like the way that trust, once damaged, may slowly return, but will leave things forever altered in the wake of its departure and return. Like the way that people change, or die, and they don't come back.
... Interlude for people who may have seen one episode and still don't get it...
So what about those crazy plots? Does Angel have a soul this week, or not? Who's Faith, and why are there two slayers running around, when there's supposed to be only one? And why is she evil now?
These are all good questions. Like any episodic fiction, Buffy jumps from interesting event to interesting event, and by this point, there have been a lot of them, certainly many more than even most extraordinary lives ever have. Furthermore, Joss Whedon and the rest of the crew are not interested in repeating themselves or just relaxing with the same comfy characters. So by this point, the plotline has has gotten a bit soapy, although without losing character consistency. Angel does have his soul back now, although he lost it for a while, and Faith was called (became a slayer) after Kendra died. Kendra had become a slayer after Buffy died, at the end of first season, although Xander fortunately resuscitated her. I suspect that when Buffy finally dies, no other slayer will be called, that the "main line" of slayers has now passed her by. The other possibility is that forever more there will be "only two" slayers, and that makes for a less-interesting episode intro. It would also unbalance the forces of good and evil by giving the rather amoral forces of the Watchers' Council a way to multiply slayers by the judicious use of an EMT unit and a vial of curare.
Faith became evil partly because of her deprived and depressing upbringing, and partly because of her weak character. She was never able to commit to joining with the Sunnydale crew, and then was unhappy that they didn't commit to her. She's envious of Buffy, and afraid of making the kind of commitment that gave Buffy the friends and loyalty that make her jealous. Also, she found out that being bad in little ways didn't have nearly the charge that being bad in big ways does. She may balk on her way down, but I'll be surprised if she has the courage to reverse her fall.
OK, interlude over, and that may not have helped you to "get it" at all... But that brings us to another reason that Buffy is so great. The characters are actually plausible enough to care about, to think about, and to talk about. Sure, some of it's over the top, and personally I'm sick to death of the Buffy/Angel romance, now finally finsihed as an ongoing plot concern. But many of theme are good people, and they're all real enough to do stupid things, selfish things, noble things, and silly things, and to make you care about the things that they do.
A final reason is that the acting is also first rate. Every scene is not perfect: after all this is a TV show made on the usual schedule. But at least twice a season there will be an episode that will resonate emotionally for few days, and where the acting evokes everything that the scriptwriters wanted. In my opinion all of the actors are very good, certainly well above normal television quality, except for David Boreanaz, who's at about average TV level, but still improving. You may feel silly after an episode when you're wandering around feeling bad or worried about a person who doesn't even exist, but isn't that kind of emotional reaction and engagement what a good story is supposed to evoke? And sometimes you'll be feeling elevated by the actions of the characters, or impressed by their good qualities, at other times, you'll be enraged by their failures.
You may not get a full feeling for some of the virtues of the show until you get fully clued into the characters, their relationships, and some of the backstory, but in the end, you too can turn into a raving fanboy like me.
Maybe you fear that kind of potential transformation, and that is why you're not watching already, but you are missing out on one of those rare instances when commercial television comes through with the real goods: a well-written, well-acted, emotionally involving story in which the characters really change, and it actually matters to them and you. really.
To quote L. Ron Hoover, founder of the first Church of Appliantology, as quoted by Frank Zappa:
"Come, on. You'll love it! It's a way of life..."