See Wikipedia's entry: Western (genre). I'm sure they explain it infinitely better than I could. But basically, this category is for movies set in the American Old West (generally in the second half of the 19th century). I'm sure there are movies that might be considered westerns on some level, which might be set a bit earlier or a bit later, or even in the present day. Though most of those set in the present (or even the future) would be more immediately of some other genre, like comedy or sci-fi. Honestly, I don't watch a lot of westerns, though there are surely some I'd like to see eventually. There will probably never be a lot of entries in this category, so I'm not sure how I'll deal with movies that are... iffy. We'll see. Also, some westerns may be considered B-movies, though it never really occurred to me to think of them as such. And some movies that might be considered westerns, I'll include under war films, if they're specifically about things like the American Civil War.
See also TV Westerns