Excellent explanations. Satire is used, as one answer said, to expose a wrong, an injustice, a flaw, a problem in order to help right the wrong, create justice, fix the flaw, or solve the problem. It's not enough that Orwell, a writer of social injustice pieces and science fiction, wrote Animal Farm to put the injustices of this era of Russian history on display. He was also trying to warn that such things can happen, have happened, and will happen again if we're not vigilant. He does couch this message in what he calls "a fairy tale" in order to make the entire concept more palatable; however, his choice of animals as characters and particularly his choice of pigs as "the bad guys" does not diminish the impact of the satire. He substitutes animals for the humans (as was pointed out above) and simulates the events of this particular Russian history in this novella. He does so to effect a change. That's what makes it political satire.
One way to define satire is to say that it is the process of making fun of some problem -- a human vice or an institution that has problems. By making fun of it, the author is trying to get people to "fix" the problems.
In this story, Orwell is satirizing the Russian communist system and its claims that it is a democratic society that is built around helping the workers. By showing the way the pigs in the story behave, he is pointing out how the elites of the Russian Communist Party set out from the very beginning to take power and privilege from themselves. He shows how they came to be no better than the capitalist oppressors that they overthrew.
This is satire because he is making fun of the way the communists claimed one thing and did things that were totally opposite. He ridicules them, in part, by portraying them as pigs. By doing this, he hopes to encourage people to think about how badly, in his mind, the Russian Revolution went wrong.
George Orwell's "Animal Farm" is a caustic satire against totalitarianism in general and Communism in particular. The political allegory exposes and attacks the hypocrisy of the Russian revolutionaries who in their effort to overthrow the Russian monarchy end up being more harsh and cruel than the Tsar himself:
No question, now, what had happened to the faces of the pigs. 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].
In the novel, Old Major represents Karl Marx and Lenin while Napoleon is the Russian dictator Josef Stalin and Snowball is Leon Trotsky and Mr. Jones of course is the Tsar. The ordinary animals especially Boxer the horse represent the exploited and gullible and uncomplaining Russian citizens - the proletariat.