Animal Farm is a fable because it is a morality tale using anthropomorphism, or animals who act like humans. Most fables use animals to convey their lesson.
A fable is usually “a brief, succinct story that is meant to impart a moral lesson” (enotes reference, fable). Orwell wrote Animal Farm to tell a cautionary tale about communism using the Russian Revolution as a backdrop. By using animals, Orwell was able to make his “fairy story” a traditional fable. Fables usually use anthropomorphism, or description of animals as humans, to appeal to children. Orwell plays on this in his parody.
Orwell also extends the concept of anthropomorphism by having some of his characters become more and more like humans. At first, the pigs oppose mankind and everything related to humans. They slowly become more and more like them, until no one can tell the difference. The other animals remain animals.
The creatures outside looked from pig to man, and from man to pig, and from pig to man again; but already it was impossible to say which was which. (ch 10)
Because Animal Farm is a fable “the reader can surmise that the story told in Animal Farm is universal, with implications for every culture or country, and that it will be easily understood” (enotes Animal Farm, style). In addition to the parody of the Russian Revolution, Orwell wanted to warn people of the dangers of capitalism as he saw them.
As well as using animals as characters, Animal Farm is also a fable because of its strong moral message. Specifically, Orwell wrote this story to destroy "the Soviet myth," as he mentions in the Preface to the Ukrainian Edition of Animal Farm. (See the first reference link provided).
By this, Orwell means that the Russian Revolution did not bring true Socialism to the people to the Soviet Union. In fact, it simply replaced one form of exploitation with another. This is shown most clearly through the character of Napoleon, who is closely modelled on the Soviet leader, Joseph Stalin, and who became just as despotic as his predecessor, Mr. Jones. There is some evidence to suggest that Napoleon is even worse: he runs Snowball off the farm, for example, and he uses his guard dogs to brutally slaughter any animal who disobeys him. Moreover, Napoleon ensures that he and the other pigs do very little work and eat the best rations while the other animals are overworked and underfed.