George's and Lennie's dream of owning their own place is part of the American Dream. The American Dream was to be able to own a home, have a job, and have a family to enjoy it with. Migrant workers during this period of time were lonely, and few of them had anyone else in their lives to care about them. This is why Candy jumps on the bandwagon so quickly to join George and Lennie in their dream. Candy is an old man who soon won't be able to work on the ranch, and he'll have nowhere to go. George, Lennie, and Candy will be a family and will have each other to care about. Their dream is the American Dream.
The most obvious way the American Dream is represented in the novel is when George helps calm Lennie down every time he gets in trouble with a story about the large farm they're going to buy one day and how they will live there and enjoy nature and work and live together forever.
They are migrant workers, and they are constantly moving from one place to the next hoping to improve their lot in life. Most of the time, they move on because Lennie has done something like murder someone by accident. He is mentally handicapped and strong beyond his understanding.