"The American Dream" is generally used to refer to the notion that anyone can rise above their station in life if they only work hard enough and use their money wisely. It's presumed to be one of the hallmarks of a capitalist society. Steinbeck questioned this assumption, often being credited with the quote: "Socialism never took root in America because the poor see themselves not as an exploited proletariat, but as temporarily embarrassed millionaires" (although the exact quote is probably a paraphrase of something else Steinbeck wrote, it does maintain the general idea).
As lowly, itinerant wage earners, George and Lennie are the epitome of the exploited proletariat. Lennie dreams of raising rabbits and George humors him, since the dream seems to make him happy. Lennie begs George to tell him about the rabbits from time to time:
"O.K. Someday—we're gonna get the jack together and we're gonna have a little house and a couple of acres an' a cow and some pigs and—"
"An' live off the fatta the lan'," Lennie shouted. "An' have rabbits. Go on, George! Tell about what we're gonna have in the garden and about the rabbits in the cages and about the rain in the winter and the stove, and how thick the cream is on the milk like you can hardly cut it. Tell about that George."
George, being smarter than Lennie, has no such illusions, though. In one of his outbursts, he tells the blunt truth:
"God a'mighty, if I was alone I could live so easy. I could go get a job an' work, an' no trouble. No mess at all, and when the end of the month come I could take my fifty bucks and go into town and get whatever I want. Why, I could stay in a cathouse all night. I could eat any place I want, hotel or any place, and order any damn thing I could think of. An' I could do all that every damn month. Get a gallon of whisky, or set in a pool room and play cards or shoot pool."
George is realistic. It is Steinbeck's statement about "the American Dream" that only Lennie, the half-wit, believes in his little rabbit farm.
The "American Dream" is commonly credited to John Truslow Adams, who first introduced this iconic idea in his 1931 book "The Epic of America." He asserted that the American Dream is "that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement."
George and Lennie are rich examples of two very different individuals trying to achieve a richer and fuller life, both with extremely varying abilities. The thing that makes them stand out against the other men on the ranch is that they have each other, and somehow having one another makes them different. Crooks and Candy are both drawn to George and Lennie because they want a piece of that too: they sense that there's something different there, something worth having.
This band of society's cast-aways pull together to pool their resources to buy a little piece of land, where Lennie can raise his rabbits and everyone can "live off the fat of the land". Just when they believe the dream is their hands, the reality of the world they live in, symbolized by Curley's wife, snatches it away. In the moment that Curley's beautiful wife dies at Lennie's hands, the entire dream of owning land is snatched away from all four of them, and ultimately, even George and Lennie's friendship is crushed when George is forced to kill Lennie.
This series of events can be interpreted in a variety of ways-that George and Lennie were chasing the American Dream by owning land, or that the real dream is having someone in your life to care about--that relationships make the man, not the property.
In either case, this is a case of the haves versus the have nots, where Curley, who is wealthy, ultimately causes the demise of Curley, Crooks, George, and Lennie. It becomes apparent that in their world, the American Dream is not open to anyone, no matter how hard they work or what they aspire to.