Buffy is the Mother of the Kick Ass Female Protagonists of Urban FantasyOh, there were kick-ass females before her and there have been even kick-assier females since. Hell, Anita Blake predates Buffy by about four years, and she's certainly earned her alpha stripes (despite enumerable flaws). But what Buffy did, in my humble opinion, is bring the kick ass female into mainstream light. The show is popular, a pop culture phenomenon, and for my generation she was the final word on unlikely female heroines.
Joss Whedon has become somewhat famous for his ability to make petite female protagonists into convincing fighters. Buffy is consciously written to subvert the cliché of the ditsy blond teenager who is the first to die in every horror movie. Her influence has made small-but-lethal ladies into a popular trope in and of itself in urban fantasy. Buffy makes up for her weak appearance with implied superpowers--supernatural strength and speed. Many UF authors do something similar, granting their heroines magical powers or gifts that bely their harmless visages. Others use brains or extreme weapons training, or some combination of all of the above. You can see why this is such a popular premise to launch a series on--it makes for such interesting and varied protagonists, with varying levels of angst and drama.
Buffy suffers from the classic fantasy heroine conflict--she wants a normal life, but she can never have one. Something always gets in the way. But she is, essentially, just like every teenage girl--and thus she goes through all of the same milestones--but on steroids. The loss of her virginity is a huge disappointment, to the tune of her boyfriend turning psycho-killer. She runs away from home and is met with a wake up call, in the form of a bizarre demonic slavery system. She finds that she wants to be popular, and become Homecoming Queen, but ends up fighting homicidal monsters all the way to the dance, only to find that she's not even runner-up. And so on. Buffy is relatable because, like most teenage girls, she feels like nothing ever goes her way and the world is against her. In Buffy's case, her life really is often miserable and the world really is out to get her. The relatability draws you in, her losses and disappointments make you emotionally invested, and her constant triumph over the monsters brings you comfort.
The fact that Buffy was so widely popular and is still remembered fondly (and continues on via comic books and so forth), means that she's often the basis of comparison for any UF heroine. Rightly so. When I read young adult urban fantasy in particular, I'm always looking to see in they included the traditional Buffy character--naïve but not stupid, seemingly and yet actually quite strong, snarky and unexpectedly smart. Maybe she has a group of friends like Buffy, or impossible romantic relationships like Buffy. Whatever variation the author goes with, there's almost always a tiny tribute in there somewhere.