What finally prompts the animals to overthrow is their owner Mr. Jones and the man's constant and chronic abuse of the animals, especially when he gets so drunk he fails to feed any of the animals. The animals then launch an attack and drive him and his wife off of the farm. The result is, at first, a seeming utopia where all the animals are equal.
This quickly grows out of hand when the pigs, especially Napoleon, starts to manipulate things to his benefit and throw out and/or attack anyone he deems an enemy.
The entire story and these actions in particular, parody and reference the events of Russia during the fall of the Tsar and the rise of Communism, specificly the rise and abuse of power by Stalin