The characters in Of Mice and Men find themselves in a hopeless situation of drudgery and insecurity. They work temporary migrant jobs, and can be fired at any time. They live from payday to payday, a hand to mouth existence. This is true of Lennie and George, the main characters, but also of most of the rest of the people in the story. Remember that it takes place during the Great Depression, a time of mass unemployment and even starvation.
So the dream is developed as a way out of this life. Lennie and George find they can, with Candy's help, buy a little farm from a couple that's broke. They can grow their own food, be safe from firings, and live with just a little security. Candy doesn't have to worry, as a physically handicapped senior citizen, where his next meal is coming from. He has a place to stay and a place to die comfortably. Lennie gets to tend the rabbits. George can stay in one place and start a life.
The dream is inevitably broken. Lennie kills Curley's wife and the whole plan falls to pieces, just as it is about to be realized. Multiply this broken dream by hundreds of thousands and you have the social misery that was the Great Depression.
P.S. You might also add the dream of Curley's wife, to be in the pictures in Hollywood, crushed by the reality of small town farm life in the Depression, and an unhappy marriage.