As Animal Farm is an allegorical novel, the characters, events and places were all developed by George Orwell to symbolize the history of the Russian Revolution.
The story begins with Old Major, a pig who has grand ideals and spouts theories of equality for all: "Is it not crystal clear, comrades, that all the evils of this life of ours spring from the tyranny of human beings?" Karl Marx, similarly, spouts theories of how all society's problems stem from class tensions.
Napoleon parallels with Joseph Stalin both dictators. Napoleon does not play a large role in the initial rebellion, but after their freedom has been established, Napoleon is introduced as one of the smartest pigs who then orchestrates the direction of the farm behind his group of dogs (the Russian Revolution equivalent of the KGB). In a later chapter, Napoleon uses the dogs to keep control by force killing animals who seem to be a threat. He raises them from a young age saying he will "make himself responsible for their eduction." He uses these dogs now to keep control through fear. This bloodshed in chapter 7 can easily be paralleled with the infamous Great Purge of the Russian Revolution.
Stalin and Napoleon both manage to reduce the effectiveness of the animal's work and productivity on the farms. Russia goes into a great famine while Animal Farm also struggles to make enough food to feed everyone.
Snowball parallels with Trotsky, the Russian leader who is run out of the government by Stalin. Snowball is also run off the farm by Napoleon who recognizes Snowball as someone who has his own ideas and his own followers. This threatens Napoleon's plan to take complete control and power over the farm. Trotsky was one of Stalin's chief rivals, and Stalin has him killed in order to put the competition away.
Other Allegorical aspects: Squealer to Stalin's propaganda, Animalism to Communism, Mr. Jones to Czar Nicholas II, Moses the Raven to religion, Boxer represents the people who buy into coumminism and work hard for this ideal only to become victim to it later on.
No matter which example you flesh out, the message is the same, Orwell points out the flaws of communism and conveys that equality cannot be achieved. People in power always want more power and will in the end abuse their powers.