Napoleon represents Joseph Stalin. Napoleon is the leader of the farm and tells the animals they are all treated the same, when they're are not. Napoleon is one of the mail villains on the farm. He slowly build up his power, then takes over the farm.
Snowball was influenced by the Spanish Civil War by Leon Trotsky. Snowball is Napoleons rival in the novel, as they are always fighting for the power of the farm. Snowball is the only pig that actually is trying to help the farm, unlike the other pigs who just want power over the other animals.
Boxer is the only character in the book that has all the good qualities of the working class. But Boxer also suffers from the working class weakness, what George Orwell called a naive trust in the good intention of the leaders.
Squealer's purpose was to show how easy it is to manipulate language and people. He uses statistics to convince the animals that their lives on the farm is improving now that the humans are gone, when they are actually still the very same.
Old Major represents both Karl Marx and Vladimir Ilych Lenin (founders of communism), who George Orwell both respected. Old Major fuels the rebellion that goes on the the book.