How does your knowledge about the former USSR affect the understanding of the story?

Animal Farm is really an allegory to old Soviet politics. Although knowing this is not essential to enjoying the book, it is certainly helpful. The themes and symbolism of the book becomes clearer when one understands that:

Old Major's Dream and Karl Marx's Communist Manifesto.

The Fall of Mister Jones = Russian Revolution of 1917

The Windmill = Trotsky-Stalin Conflict

Battle of the Cowshed = Russian Civil War

The list goes on but the motif of old Russia runs through the story.