There could be a number of reasons for this. One that comes to mind is that the story has a lot of qualities of the fable which usually uses animals with human qualities to make a point. (Consider Aesop's Fables such as "The Hare and the Tortoise" and "The Fox and the Grapes").
Another reason might be to make those he was targeting appear foolish. What nicer way to do this than call the leaders "pigs"? Sheep represent the masses that are easily led astray and these could be seen as an allusion to some of Jesus's New Testament teachings. Also, making the characters animals makes it easier to not have to define human features that may mislead the reader into thinking of an unintended target for the satire.
The allegorical satire of Animal Farm is amplified by the use of talking animals There is a dark moral in Animal Farm, but it is accepted because it is presented in a humorous, nonthreatening way.
The idea that animals could work together cooperatively to overthrow their human bondage is laughable and really ludicrous if you think about it deeply. So, what perfect way to show the inequality of class in society than by showing how the pigs eventually took over the idylic farm and became totalitarian rulers exactly like the humans had done.
By using animals, Orwell was able to avoid the psychological implications that would have come up had he used human beings as characters. He is able to use the pigs to degrade the Russian Communist leaders, the sheep as the masses, the horse as the steady plodding worker who carries more than his fair share of the burdens. People who were accustomed to farm animals and their roles in farm life would have been able to relate to the attributes that Orwell gave to these animals.