This is a good question. It is first important to define what anthropomorphism means.
A good definition of anthropomorphism is giving human qualities to other things, whether these be gods or animals. In the case of Animal Farm, we are dealing with animals.
So, we can say that the whole book is an anthropomorphism. It plays the most important role in the book. At first the anthropomorphisms are small. The animals speak, some well, others not so well. Then the anthropomorphism becomes more significant. Some animals are able to read and they become very eloquent like Squealer. Then the animals are able to build things like windmills. Finally, in the last few pages of the book, the pigs turn into humans. In this sense, the anthropomorphism is complete. In fact, there is a bit of irony. The anthropomorphism is so complete that is it no longer an anthropomorphism, because the pigs are now humans.
In a word, anthropomorphism undergirds the book. And the message is that the pigs become what they set out not to become.
George Orwell's allegorical depiction of animals as substitutes for people, Animal Farm, is a classic example of anthropomorphism, which is defined as the attribution of human characteristics to non-human objects. Indeed, anthropomorphism is entirely the point of Orwell's novel. What makes Animal Farm particularly fascinating is that, while attributing human characteristics to animals, it also includes humans, mainly Mr. Jones, the head of the farm where the story takes place. Humans represent oppression, and the animals conspire to overthrow their oppressors, becoming ever more human-like in the process. Early in Animal Farm, Old Major, a boar and the most respected animal on the farm, gathers the rest of the animals and gives a speech on the need for the animals to be liberated from their human oppressors:
No animal in England is free. The life of an animal is misery and slavery: that is the plain truth....
Because nearly the whole of the produce of our labour is stolen from us by human beings. There, comrades, is the answer to all our problems. It is summed up in a single word—Man. Man is the only real enemy we have. Remove Man from the scene, and the root cause of hunger and overwork is abolished for ever.
While depicting man as the source of the animals' problems, the animals are themselves depicted as human-like. The revolution is successful, of course, and the animals, freed from domination by the farmer, now proceed to conduct themselves in an entirely human fashion as they establish what they think will be the ideal collective—a plan that fails when the pigs, greedy for power, begin to corrupt the system.
Animals are substitutes for people in Animal Farm. While people exist (they have a recurring role as counter-revolutionary forces that threaten to return to power), it is the farm animals that plot revolution, seek to establish an egalitarian order, and eventually descend into autocratic excess. The animals represent the masses and those who would seek to rule over them. By employing such a literary device, Orwell is able to illuminate distinctions among mammals, with one particular species, the pig, maneuvering for supreme power in the manner of the Bolsheviks and their most ruthless embodiment, Joseph Stalin.