Soon enough, supernatural elements come in, things make less and less sense, and by the end of Season 1, you don't have much of an idea of what's going on. By the end of Season 2, you have even less of an idea of what's going on, and the ending leaves many questions. But don't worry, they came out with a Season 3 many years later!
Season 3 is even more confusing than the first two. There's a talking brain tree, a scary being in a box and a lot of things happening at once. It seems as if some of the questions from Season 2 are answered, but not necessarily in a way that makes sense.
The charm of Twin Peaks is that while it feels like something nostalgic from a bygone era that never was, it also feels like a strange dream. Playing on fears surrounding identity and the unknown, there's something just deeply wrong about it. This is what makes the show so interesting as a work of horror/science fiction/fantasy. (Still not sure which one it is.)