A cult film typically, but not always, is one that has a devoted fan base but isn't universally popular. Very often it's a film that wasn't successful on first release, or that the critics didn't like but some of the public did. Over time a cult film can get more and more popular, but it can still be considered a cult if it is a bit non-mainstream or indeed downright strange, and especially if it has a hard core of, often rather obsessive fans. A good example is The Wicker Man, which was very much cut before it could be released, was derided by many critics and treated as rubbish (literally: One version of it actually got thrown away) but for many years was consistently voted for by the British public as the film they most wanted to see on TV. It also got a whole lot of legends and odd stories surrounding it, which is another hallmark of the cult film.
You can find more features of the typical cult movie here.