This dream, I think, is the American Dream. Before the Great Depression, this dream seemed real: even immigrants who didn't speak English could dream it. This dream was based on a strong work ethic. But now, in the midst of near famine and economic upheaval, this dream seems no longer true. A strong worth ethic alone does not achieve it.
George and Lennie, no matter how hard they work, will not achieve their Dream Ranch. George, in this quote, I think, knows it. He knows that the earlier American Dream is a false one now. It is the dream that lures thousands to the promised land of California only to disappoint them, leave them homeless, and destroy their families.
In California, there is simply too much competition and not enough workers' rights for this dream to be valid any more. The dream is only valid for the bosses (The Boss and Curley) and not the workers (Lennie, George, Slim, Candy, Carlson, Crooks) or the minorities (Crooks) or women (Curley's Wife).
In short, The Boss lures these migrant workers to his ranch in search of a dream and hope, but--in the end--they only find lice, abuse, cruelty, and death.
In Chapter One of John Steinbeck's novella, Of Mice and Men, George complains to Lennie that he is a great deal of trouble.
I could get along so easy and so nice if I didn't have you on my tail. I could live so easy and maybe have a girl.
By taking care of Lennie, who is, after all, the keeper of their dream, George commits himself to his mentally diminished friend. And, by doing so, he eliminates other possibilities in his life such as having a relationship with a woman, or having no one to worry about but himself. By partaking of the dream with Lennie, George directs his happiness as contingent upon the fulfillment of this unrealistic dream. When Lennie gets into trouble, inevitably, George is left isolated and bereft of friendship as well as hope; For once having had a dream that cannot be realized. George is all the more alone as with the dream, so goes his friend Lennie.
To me, we can see the truth of this quote in George's life because his dreams give him hope, but they also lead him to greater unhappiness when they are dashed.
Because of the dream that he shares with Lennie, George goes through most of the book with hope. He believes that one day they will be able to live lives that are free and independent. This gives him something to aim for.
But when the dream is ruined at the end of the book, George is more devastated than he would have been if he had not had any hope to begin with. When you have a dream, you can have hope -- you can hope your dream will come true. But you also set yourself up for much more disappointment. People who have no expectations or hopes are not disappointed no matter what happens.