What are some examples of allusions in the book Animal Farm?
A reader can interpret allusions in a literary work whether or not they were intended by the author. For instance, since Animal Farmis a satire about a communal or socialist society gone wrong, this could be interpreted as an allusion to the Cuban Revolution. Having written the book in 1949, Orwell was clearly not making references to the Cuban Revolution, although it did occur shortly afterward (1953-59). The point is that an allusion can be inferred from the reader's perspective.
However, if you want the allusion that Orwell had in mind when he wrote Animal Farm, the most significant allusion is with the U.S.S.R. (now Russia). Napoleon represents Stalin and Snowball is Trotsky. Animalism began with great hopes but ended up being as oppressive as the regime the animals had revolted against. The allusion is to the failed communist project in the U.S.S.R. Orwell couldn't agree with Stalin's pact with Hitler, not to mention Stalin's deportation of hundreds of thousands (or perhaps millions) of Russians.
Orwell meant this story to be an allegory as well as an allusion so it could serve as a warning against any potential subsequent oppressive states.
In literature, an allusion is an "indirect reference" to a person, place, event or idea. In Animal Farm, the allusions are plentiful. The setting of the story, for instance, is an allusion to the Soviet Union which experienced a revolution in 1917. The leader of this revolution was Vladimir Lenin who inspired a group called the Bolsheviks to seize power, just as Old Major does in Chapter One.
Like the Bolshevik leaders, the pigs take charge of planning the revolution and its aftermath. Snowball is an allusion to Leon Trotsky, a revolutionary intellectual, who was famously exiled from the Soviet Union in 1929, just as Snowball is chased off the farm in Chapter Five. Similarly, Napoleon is an allusion to Joseph Stalin, the dictator responsible for Trotsky's exile. Through the character of Napoleon, Orwell alludes to many of Stalin's humanitarian crimes during his rule over the Soviet people. The Moscow Trials of 1936-1938, for instance, are represented through the rebellion and slaughter of the hens in Chapter Seven.