The three main pigs are Old Major, Napoleon, and Snowball, and they all are said to represent one of the three major figures of the Soviet Union.
Old Major is slightly different from the other two because Orwell was said have based him on two people: Vladimir Lenin and Karl Marx. Though Old Major dies in only the second chapter, his speech outlines the principles of what will become known as animalism, which shares many of its ideas with Marxism. Similar to Lenin, he uses his principles to start a revolution.
Orwell based Napoleon on the Soviet dictator Josef Stalin. Like Stalin, Napoleon abuses his power and uses the principles of animalism to benefit him, and those close to him, and oppress everybody else. He will do anything to keep his power, including killing the other animals. He even surrounds himself with his own private army made up of dogs he brought up himself from puppies.
Orwell based Snowball on the Soviet political theorist Leon Trotsky. Like Trotsky, Snowball opposes Napoleon's ideas and causes unrest among his comrades. He puts the animals first—for example, it's his idea to build a windmill—and so becomes a threat to Napoleon's authority. Napoleon forces Snowball into exile, just as Napoleon did to Trotsky, and then destroys his reputation, telling the other animals that Snowball was a traitor and had always supported Mr. Jones.