What is the significance of Willy trying to kill himself in Death of a Salesman?
Willy had a false idea about most aspects of his life: He thought they were in really dire straits when, in fact, the day of his death his wife had posted the last house payment, and said that they were finally "free." However house-debt free they were, to Willy nothing was ever enough.
When he took his insurance policy it was not for the reasons why rational people would take it. It is RICHness what Willy sees as "the American Dream". To have it all, or to have nothing. Even if before his death he had already paid his home off, the truth is that this, to Willy, is part of his obsessive connection between money and success. Hence, instead of thinking of a life insurance policy as a way to leave his family save, he committed suicide for Biff to cash in the policy, start a business, and become rich.
In all, Willy had a wicked fascination with money and success which led to the twisting of reality, and the devaluation of the things that matter the most.
The previous post was very thorough. I would only like to add how the meaning of Willy's suicide represents the crushing weight of one's dreams. Willy is trapped underneath the pursuit of the American Dream. This idea is that one can "be somebody" and this is measured through financial success. The suicide for the life insurance money is a way that one can see how twisted the desire for economic success can turn out to be if improperly guided. Willy is not greedy as much as he is galvanized by the idea or hope that he can "become" somebody or something. This is measured, in his mind, through the acquisition of wealth and the only way he can see this happening is through his own death. His suicide represents how the American Dream can turn out to be something of nightmare proportions if not fully understood and placed in an appropriate context.
In the play Death of a Salesman Willy Lowman has spent his life going over the road as a salesman. In his youth he was probably a mediocre salesman who did his job as directed. He was able to purchase a modest home mortgage which he has paid upon with his draws from his sales. He raised two sons and has a wife. He has struggled to attain the American Dream of owning his own home outright and being able to provide for his family.
Willy's sales abilities have declined as the market has changed. Although he lives a fantasy life with his family by telling them everything is going well, he internalizes that he is a failure. He has had to borrow money to pay his bills from his boss's son who has now taken over the business. He recognizes that he will be fired soon because he is a drain on the company.
Willy has difficulty coping with the pressure and failure. He has an insurance policy that, in the event of his death, will enable his family to pay off his mortgage. He keeps trying to kill himself so that he can realize the American Dream for them and not have to face the shame that they discover his failings.