"I would love to be upstairs watching TV or gossiping about boys or, god, even studying! But I have to save the world. Again."
-Buffy, "Becoming (Part 2)"
It's not unusual for a series to take a while to find itself. Buffy had it especially tough, because the first season had to walk a lot of difficult lines: between comedy and drama, between high school and horror, and perhaps most importantly, between faithfulness to the film and striking out on its own. All of this had to be done without audience feedback because the first season was produced entirely before airing. For this reason, while the first season is quite enjoyable and has a lot of the right ingredients, it isn't consistent in finding the right balance between them.
Perhaps that's why season two is so satisfying: it's the season when Buffy's potential for greatness really activates. I don't think it's the best season, whether you measure in terms of its overall plot or the average strength of its episodes (I think those honors go to seasons three and four respectively, but we'll see whether I still feel that way in a couple months). It's the pleasure of learning what the show, what it can be, that makes Season Two so great.
At the outset, I was wondering whether I would notice a single moment when Buffy "became Buffy." It didn't really happen like that. While "School Hard" makes a strong contender of itself, its momentum is squandered by the two subpar episodes that follow it, "Inca Mummy Girl" and "Reptile Boy." The momentum is an important part of what makes Buffy great, and the show isn't at its best unless that momentum is there. Even standalone episodes have to preserve that momentum, if not through continuing the plot then by deepening our understanding of the characters.
And that's pretty much what happened in season two, isn't it? Take Cordelia for instance. By the end of the season she seems much more like an integral part of the Scooby Gang and of the show. Yes, this is because she's dating Xander, but that wouldn't count for much if we hadn't gotten to know her better, largely through standalone episodes like "Some Assembly Required," "Bewitched, Bothered and Bewildered," and "Go Fish." The latter features a surprisingly touching moment where Cordelia, believing that Xander has turned into a fish monster, promises that they can still have a relationship. And we actually believe her when she says this. How far she's come since the beginning of the season.
So the reason Buffy became so much greater in season two is because of the way it began to build, making use of the ingredients that were already there and turning them into something greater than the sum of their parts. That being the case, I can't pick out one episode where Buffy suddenly came into its own. I can only pinpoint the moment when, during my first viewing of Buffy, I suddenly became conscious of it: not the moment where Buffy grew up, but rather the moment when I realized that it had already grown up.
That moment was "Innocence," when Angel lost his soul. After watching it, I was shocked, but simultaneously surprised at my own shock. It was surprising to me that the show could affect me that much, and it made me realize just how much I had grown to care about the show and its characters. I had been watching the first two seasons on borrowed DVDs, and up to that point I was unsure about whether I was in it for the long haul. But after watching "Innocence" I decided that I had to buy the complete series.
Which just about sums up my thoughts on the second season of Buffy: It's the season where it finally starts getting to me, getting into my head, and making me feel really invested in what's going on. There's more that could be said about it as a season, but that's certainly the main thing as far as I'm concerened.