Having a place of one's own can give meaning to a person's life. I think that may be the way to express the answer to the question here in a few words and I think this is the way "place" and "ownership" can be said to function ideologically in Of Mice and Men.
Without anything of their own, all the labor that George, Lennie, Candy and Crooks put in on the various ranches that employ them is, essentially, work thrown away. Yes, they get paid, but they are employed to help someone else build a life and get rich. There is nothing for them in the work that they do.
You have identified an important theme in Steinbeck's work as a whole. Part of the tragedy of novels like Of Mice and Men and also Grapes of Wrath is the way that families and individuals become dislocated from their own land - their roots, and are forced to travel and journey to strange lands in order to live and find work. Belonging is essential to sustain us, to give us pride and a sense of status in the world and lastly to enable us to find others that we can belong with. In the novel, George and Lennie belong to each other, but to truly belong they need their dream of a farm together, where they can live happily and have somewhere where they belong. The tragedy of Steinbeck's novels is that dislocation from home or our land inevitably ends up with dislocation with the relationships that are important to us. Having somewhere to belong prevents that schism.
The idea of belonging in the novel 'Of Mice and Men' by John Steinbeck, relates to the theory of 'attachment' in psychology. For most human beings, having a central place they can return to, ideally with loved ones or supportive friends present also, contributes towards their feelings of calm, relaxation and security. Such a place would ideally be one which provides safety,shelter,food, warmth, affection and earning capacity. Not all those elements are always present - sometimes it is enough to live in an RV or trailer park, as long as family or the other things are present. Some nomadic people are happy to pack up and take most things with them - as long as they have support they are happy. However, George and Lennie only have each other and sometimes that's even a liability - whatever 'attachments' they had in youth are gone and that leaves them adrift in a hostile, unpredictable world. That is why they yearn for 'centredness' or the security of a place of their own.
I would think that one of the most powerful lessons of Steinbeck's work is the idea that individuals have to possess a sense of belonging. Part of this is definitely physical. When individuals have to wander from life to life, different form of physicality to different form of physicality, their ability to better understand themselves and others becomes impacted. There has to be some notion of grounding at some point and level where individuals can feel comfortable enough to call it "home" or know that this is where I belong. Despite lacking this, Lenny and George do a fairly good job of providing the belonging to one another. Certainly, Lenny sees George as essential to his conception of belonging. Yet, George does envision Lenny as a part of his own conception of belonging, a vision that appears in George's dreams and whose faintest touch can be felt in the relationship they both share.
The answer to this question lies in the character named Candy in "Of Mice and Men." An old, disabled ranch hand who is unable to stop the killing of his old friend and dog, Candy realizes that he soon will outlive his usefulness and, perhaps, go the way of his old dog. But, when he hears of Lennie and George's dream of owning a ranch and a house, he is sweetly hopeful, offering his savings to the men. For, with part ownership, he would not fear isolation and poverty, or abandonment.
From owning land, too, there is a sense of pride. The itinerant men of the Great Depression belong nowhere, they had nothing and lived in fear of losing a job, for they could not survive without any money. There is a constant stress put on these men who must few the next man as a threat to his job or security. But, if one has a place of his own, he must answer to no one else. In the early part of the novel, George explains the position of thes men in the world:
'Guys like us, that work on ranches, are the loneliest guys in the world. They got no family. They don't belong no place, They come to a ranch an' work up a stake and then they go into town and blow their stake, and the first thing you know they're pounding their tail so some other ranch. They ain't got nothing to look ahead to.'
Clearly, owning land and a home provide security; these cannot easily be taken from a person. Pearl S. Buck's "The Good Earth" testifies to the solid good that comes from owning land, since Wang Lung's land is the only thing that helps his family and him recover after the Great Famine, and the return to it is what drives him to continue living.
People need to belong, because no one is created to be alone. Even when a person is born, he or she is taken care of, and this pattern continues. There might be a false sense of independence, but it does not exist. We are all created for community in so way or other. This is why Aristotle stated that we are all "social" animals. The level of involvement in community might differ from person to person, but in the end people need to belong. In the final analysis, I think this is what is means to be human, in part. The sense of belonging is hardwired into us, in my opinion. Without it, people will be dysfunctional.
I believe that all people want to belong, although I am not sure that it is all that necessary to belong to a given place.
I would say that a feeling of belonging makes people feel secure. When we feel that we belong in a certain place, or with certain people, then we can reduce our stress levels by being in that place or with those people.
Like I said, though, I don't think it has to be a place. I, for example, had lived in nine different houses or dormitories by the time I was 17 years old. But that wasn't a big deal because I knew that I belonged wherever my family lived.
Now, I have lived in the same house for 11 years and the feeling I get from that is not really different.
So I would say that we need to be able to feel safe, to be able to relax. But it doesn't have to be a specific place.
for me personally we are son of the planet earth and that's why we are named human. no passport, visa and authorisation should be needed to travel around this planet. but......