Mr. Jones was a lazy drunk and exploited the animals at Manor Farm. So, the animals, inspired by an eloquent speech by the aging and respected pig Old Major, decide to drive out Jones and take over the farm for themselves. They establish a new government, based on seven commandments of "Animalism", written on the side of the barn, that purport to protect the rights of the animals.
It isn't long before animals are vying for power and exploiting that power once they have obtained it. The pigs are the most clever, so they take control, and end up revising each commandment to their advantage, grabbing more authority for themselves and becoming more and more like Mr. Jones and other human farmers as time goes on.
The other animals eventually find themselves as oppressed by their new pig overlords as they were by their former human masters. After numerous lies, deceptions, and thievery, the pigs modify the final commandment from "All animals are equal" to "All animals are equal, but some are more equal than others". The citizens of animal farm realize too late that they have traded one master for another equally bad one.
Animal Farm is George Orwell's first great work of fiction and it endures over 70 years after its initial publication. Orwell originally wrote the story as an allegory about the Russian Revolution and how Stalin eventually twisted its goals to his own ends; but Animal Farm is ultimately about how absolute power corrupts absolutely and this lesson can be found in any part of the world or political spectrum.
Napoleon the dictator pig uses many strategies to maintain control - from repeating lies that draw his enemies in an unfavorable light to using violence to suppress any voices. It's frightening how much these tactics are still used successfully today.
Orwell followed up Animal Farm with his classic 1984, another dystopian novel with a similar theme about the corruption of power; but Animal Farm does so more subtly, without the need for a closing speech to explain the methods and motivations of the ruling class. Animal Farm is shorter, but more imaginative than the later work. Animal Farm is a simple fable with a simple plot packed with symbolism. The characters are based on real figures of Soviet Russia (Old Major = Karl Marx; Snowball = Leon Trotsky; Napoleon = Joseph Stalin; Mr. Jones = Tsar Nicholas II), but the story works even if the reader is unfamiliar with that history.