Several times in the book, like a chorus, George describes the small house and the farm that he hopes to own with Lennie. His vision is idyllic. They will live off the fat of the land. The house and the land won't be too big, but hey will be self-sufficent. They will work, rest, and have security. Here is one of the descriptions:
“Sure, we’d have a little house an’ a room to ourself. Little fat iron stove, an’ in the winter we’d keep a fire goin’ in it. It ain’t enough land so we’d have to work too hard. Maybe six, seven hours a day. We wouldn’t have to buck no barley eleven hours a day. An’ when we put in a crop, why, we’d be there to take the crop up. We’d know what come of our planting.”
From this description, we can make a few points. First, George and Lennie as migrant workers do not have a place to call their own. So, to have a house is to have a place they could call home. This is a huge dream for migrant workers. The landless will have land, and the homeless will have a home.
They also won't have to work too much. Currently, they are working eleven hours a day, truly backbreaking work. Also, they will have protection from the elements. Later on George even entertains the idea of having visitors. Hence, there is also a note on friendships.
All of these dreams point to George's aspirations.