In the early 1920s, Lenin started to get sick—deathly sick. And that meant one communist party was about to need a leader. Josef Stalin (Napoleon) and Leon Trotsky (Snowball) both waving their hands around in the air and shouting "Pick me! Pick me!"
One major difference between the two (aside from the fact that one was a possibly psychopathic dictator) is that Trotsky wanted to spread the Revolution in other countries, while Stalin wanted to hunker down and consolidate power. But only Stalin had the power to make his vision happen: he was General Secretary of the Communist Party, so he was able to convince people to support his campaign against Trotsky. After Lenin died, Trotsky was exiled. By 1928, Russia was Stalin's.
In Animal Farm, this whole is represented by the argument over the windmill. Whose idea was it to build the windmill?