How did Animal Farm demonstrate graphically Marx's theory of history and communism?
Animal Farm is a satirical depiction of the Soviet Union under Stalin, which is a pretty far cry on a number of levels from anything predicted by Marxian theory. In some ways, this is the point. Old Major's speech in Chapter One serves as the ideological basis for Animalism. He argues that man is the source of animal misery, and that by overthrowing man, a just and equitable society can be created.
...In fighting against Man, we must not come to resemble him...All the habits of Man are evil. And, above all, no animal must tyrannise over his own kind. Weak or strong, clever or simple, we are all brothers...All animals are equal.
In this, Orwell is drawing parallels with the thought of Karl Marx, whose nineteenth century writings were the foundations, with significant alterations, for Lenin and the Bolsheviks. Napoleon, while ostensibly motivated by the teachings of Old Major, eventually corrupts these teachings to create a society as unequitable as the one he overthrew. Similarly, Stalin's actions were quite far removed from the theory of Karl Marx. One significant difference, it must be observed, is that Old Major died just before a revolution that he predicted. Marx had been dead for over thirty years before the Russian Revolution, which he had seen as highly unlikely given the lack of a fully developed industrial proletariat. But the parallels drawn with Marxian theory, including its corruption in the hands of Stalinism, are explicit.