For Lennie, the dream is to be able to enjoy the soft things like mice and rabbits without anyone telling him not to, or worrying about hurting them. For George, it is independence.
When George and Lennie are traveling to the next job at the beginning of the story, Lennie remembers a “lady” who gave him mice.
Lennie sat down on the ground and hung his head dejectedly. "I don't know where there is no other mouse. I remember a lady used to give 'em to me- ever' one she got. But that lady ain't here." (ch 1)
George tells him that the “lady” was his Aunt Clara. For Lennie, he just remembers the softness of the mice. Lennie tells him “you ain't to be trusted with no live mice.”
The dream of the rabbits is one that George has created to give Lennie hope and distraction. No matter how bad things are, they can remember the rabbits and how someday they will live off the fat of the land. The dream is just as important to George as it is to Lennie, even though he is aware that it is mostly impossible.