Since Animal Farm is an allegory based on the problems resulting from Russian Revolution, and its subsequent oppressive communist state, one of the messages of the novel is about how power can often lead to corruption and oppression. Even when a revolution is done with the best intentions, all directed toward the greater social good, it can devolve into a government which is just as bad (or worse) than the oppressive regime which it replaced.
Other messages or lessons of the novel include the means by which a government rules and/or oppresses its people (or animals in this allegory). When the revolution begins, it is to establish the law of the land that all animals are equal. However, over time the pigs (leaders) clearly put themselves in a higher position (under Napoleon) and this reestablishes a hierarchy (which was what the revolution was supposed to have eliminated). This hierarchy divides the animals; thus, they are no longer all equal.
The novel also shows the ways a group/government can manipulate and brainwash its citizens through the use of propaganda. Napoleon and Squealer constantly change the seven commandments in order to suit their increasing power. By the end of the novel, the commandments read less like a document stating the equality and happiness of all animals, and it reads more like the establishment of the privileges of pigs over all animals. Napoleon and Squealer not only change the commandments (usually acting as if they had never been changed); they also change history to suit their narrative. Snowball had been the hero of the Battle of the Cowshed, but in order to praise Napoleon and criticize Snowball, Squealer gradually changes the story, eventually making Napoleon the hero of the battle. At the end of Chapter 5, Squealer says:
And as to the Battle of the Cowshed, I believe the time will come when we shall find that Snowball's part in it was much exaggerated.
Using propaganda and fear, the novel shows how even a revolution with intentions of total equality can devolve into an oppressive state. The further message is about the tendency for power to corrupt. As Napoleon's regime gained power and privilege, the corruption increased as well.