There are several references from various characters in Miller's Death of a Salesman to planting gardens and building homes. Why is the home important to them?
Arthur Miller's Death of a Salesman is about achieving the American dream—but here, it is about the Loman men failing to achieve this dream. Perhaps it is not so surprising in that the family is unable to function in a healthy way. As I see it, planting a garden speaks to hope: living things that we plant introduce new life into our lives, and the growth of what we have planted with our hands is particularly gratifying. Willy talks a lot about planting a garden, but it never seems to work out. The planting may be symbolic to Willy of having children and watching them grow. However, they have not turned out the way he expected. He was sure they would be greatly successful, especially Biff.
Unrealistically, Willy expects things of his son that he cannot attain himself. We can never be certain that Willy was ever as successful as he says he was: he is an unreliable narrator. He lives in a dream world, talking repeatedly to his dead brother Ben as if he were there. Willy's lack of connection to the real world can be seen in not only his illusions regarding Ben, but also in his expectations of his boys. It is possible that he is trying to live vicariously through them, but Willy is very much to blame for what he sons have become—as much as for what they have not become.
Biff discovered his father having an affair while on a sales trip. Seemingly Willy has brushed it aside—for he acts as if Biff is purposely trying to thwart him. Biff, who greatly loves his mother, cannot forgive and forget Willy's infidelity and betrayal of Linda. Linda is unaware of what has caused the father and son's broken relationship.
Hap simply wants to be wealthy, on his own, surrounded by a lot of women. This fantasy may also be the result of Willy encouraging his son to be a man—and this scenario that so appeals to Hap is in keeping with what some men at that time (and even today?) perceived as success.
The Lomans as a family is a sham. Linda tries to get the boys to appreciate their father.
LINDA: Either he's your father and you pay him that respect, or else you're not to come here.
Linda also is doing all she can to keep Willy (who is emotionally unstable) from taking his life. Linda's endeavor to "make" the family normal is seen in how she speaks to Willy—knowing of how unstable he is:
Willy...Few men are idolized by their children the way you are.
Family dysfunction is seen again when Hap speaks of his father's concerns and worries. Biff, knowing things about Willy that Hap doesn't know, asks...
What's he say about me?
HAP: I think the fact that you're not settled, that you're still kind of up in the air...
BIFF: There's one or two other things depressing him, Happy.
HAPPY: What do you mean?
BIFF: Never mind. Just don't lay it all to me.
Some essence of Biff must remind Willy not so much of what Biff knows, but that something is off between them. Linda tells Biff that Willy has been a little addled for some time—wandering off in his pajamas, etc. It only seems to get worse when Biff comes home. Linda does not understand why Biff and Willy fight, and Biff cannot tell her.
Linda adores Willy and would do anything for him. The boys aren't really motivated. Biff knows Willy's secret. Willy is delusional. They are related, and "play" at being a family, but it's not real. Though they don't understand the problem completely, they feel the "loss" of what they imagine family should be. Home is a safe place, but not at the Loman house.