A short story is short piece of literary work; this is the broadest possible definition. This rules out novels, historical books, and other longer works. As for length, there is considerable debate. In other words, we need to be flexible here, because length is determined by the author.
Short stories also have a few other characteristics, which most writers agree upon.
First, short stories are usually fiction. Hence, you normally do not have non-fiction short stories. Second, short stories usually have a pointed message that is thought provoking. Not all short stories have morals, but there can be a moral with a twist.
Apart from these very basic characteristics, the format of a short story is pretty flexible.