People in power tend to manipulate those underneath them: Napoleon took advantage of the other animals by forcing them to work even more than they did when Jones was there. He did this by using propaganda and Squealer's speeches that reported facts and figures.
Society should be careful of it's leadership and challenge leaders: We see Clover wonder several times if things are changing. We actually see the pigs change the rules as time goes on. If a leader was doing something wrong, they should be held accountable to do things right.
Society needs a balance of power: The animals thought that if they had the chance to run themselves, they could feel free and be happy. It turns out that because they didn't all share in the decisions, they were trampled on and taken advantage of.
Orwell's main messages:
1. All revolutions are betrayed eventually. The idealism they begin with will disappear and society will become corrupt.
2. Those who take power (the pigs) will take more and more and they will misuse it for their own selfish benefit.
3. Do not trust politicians. Boxer trusts Napoleon, but Napoleon sends him to his death.
4. Any political system will become corrupt if they (the politicians) are allowed to get away with it. Think of how the pigs gradually change all the commandments for their own benefit.
The novel is really an allegory about the Russian Revolution and the what happened in the Soviet Union up to 1945. If we add this perspective, we can say that Orwell's other message is
1. Stalin and the Communist Party (Napoleon and the pigs) betrayed the ordinary people of Russia in the name of equality. Stalin murdered millions of his countrymen - this is mirrored in the scene where many animals are slaughtered in the barn.
Have you studied the book as an allegory? If not - feel free to ask more questions!!