George Orwell himself called Animal Farm a fairytale. A fairytale is a story about magical and imaginary happenings, creatures, and places. Animal Farm does fit that definition, as in real life animals don't talk, plan, or involve themselves in revolutions, and pigs don't turn into people. A fairytale is also a story that is fantastic and could never happen, so Orwell is being ironic as well as factual, or saying the opposite of what he means, in calling the book a fairytale.
This leads to the second genre the book falls under, which is allegory: an allegory is a story that mirrors reality but in a disguised way to deliver a lesson. In Animal Farm, using animals to depict real people like Trotsky (Snowball) and Stalin (Napoleon), Orwell is depicting what he believes has already happened (what is the reality, not a fairytale) in the Soviet Union: what started out as a "people's revolution" has turned into a brutal tyranny in which people are worse off than they were before.
This leads to a third genre Animal Farm fits: the fable. A fable is a story, usually using animals, that has a moral lesson for humans. Animal Farm is a cautionary tale with the moral that if people aren't careful about guarding the true meaning of their language and their freedoms, they will be oppressed.