Well, the Hellmouth acted as sort of a monster magnet. Demons and the like were drawn to it, hence why Sunnydale was such a hotspot for activity.
Which is a nice narrative device, yet we know Buffy was originally in LA, where she apparently had no trouble finding vampires to kill - and of course, Angel ends up there, also having no trouble finding bad guys to go up against. I gather the Hellmouth is an explanation for why so many apocalyptic events go down in Sunnydale, all fine and dandy, but there is little to explain how and why so many monsters exist in general, and why, if they do exist, the world seems pretty much like our own, except it comes with monsters. My problem with that is, our world plus monsters really wouldn't look like our world. I don't know, it seemed to me that Angel did a pretty good job of riffing on that idea, but Buffy is a little more obviously mixing horror movie and superhero tropes. I guess the genre-bending that Whedon is known for is just in its early stages here, and he gets a little smoother at it as he goes along, maybe? Buffy at this point feels a little clunky.