Old Major's dream is a stand-in for Karl Marx's Communist Manifesto.
Animal Farm opens with the news that old Major, "the prize Middle White boar" (1.2), has called a meeting to share a dream that he's had.
Wait, come back. It's not your usual "let me tell you about this crazy dream I had last night." It's a little more, "I have a dream": Old Major's dream is about equality. He tells the other animals that "Man is the only creature that consumes without producing," and he encourages them to "work night and day, body and soul, for the over-throw of the human race" (1.9, 11). In short, he explains that men have been taking advantage of them for years, and that it's time for the tyranny of man to end. His message? "Rebellion" (1.11).
In other words, Old Major's dream is a simplified version of the Communist Manifesto.
In 1848, Karl Marx and Frederick Engels published the Communist Manifesto, which laid out the basic principles of what we now call communism. The basic idea of the Manifesto was capitalism was seriously flawed. The workers never saw the products of their labor because the capitalists—the people who owned the means of production (factories, land, etc.)—claimed the profit for themselves. In other words, workers grew the grain; the landowners took it. Workers made the chairs; factory owners sold them and kept the profit.
So what? Isn't that how the world just works? Well, yeah. Because we live in a capitalist system. (Most of us, anyway.) But Marx's point is that the landowners and factory owners don't produce anything. They might hold the deeds or buy machines out of their company's earnings, but they're not actually doing labor. For most people, that's not a problem—that's just the way the world works.
For Marx, it was a big problem and it led to massive exploitation of the workers. He said that if common workers could overthrow the capitalists and claim the means of production for themselves, then all the workers of the world could live in peace with one another. At the end of the Manifesto, Marx declares, "The proletarians [common workers] have nothing to lose but their chains. They have a world to win. Workers of the world, Unite!" Old Major essentially ends his speech the same way with his final call to "Rebellion!"
Problem: Marx and Old Major are better at criticizing the existing system than at proposing a new one. After the rebellion, the big question becomes: now what?
One question is, why Russia? Marx and Engels wrote the Manifesto in 1848, when people all over Europe were revolting against monarchies. But the first communist revolution didn't take place until sixty years after the Manifesto's publication—and not even in Europe.
Well, Russia was a little different from Europe. Europe had basically gotten rid of feudalism by the seventeenth century. (Feudalism is the economic system that capitalism replaced, in which major aristocratic landowners owned not only the land but the serfs who worked it.) But Russia's serfs weren't freed until 1861. The country had an enormous and kind of angry peasant class; plus, its monarchs (the tsars) were out of touch even for monarchs.
In other words, the barn animals are itching to overthrow Mr. Jones.