Allegory is when something has a literal meaning and a second meaning which is metaphorical.
A satire is a when a writer takes a serious subject and makes fun of it yet still keeping the seriousness to it.
A fable is a brief, succinct story, in prose or verse, that features animals, plants, inanimate objects, or forces of nature which are anthropomorphized (given human qualities), and that illustrates a moral lesson (a "moral").