"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.