There are elements of delusional and unstable behavior in Willly from the beginning of the play. He hasn't been able to drive safely for a while (although we do not know how much of his problem is inability to drive and how much is realted to his desire to kill himself), yet he heads out on the road to Boston to "represent" his company. There is evidence that he has not been able to sell much recently (he has been moved from salary to commission), but he continues to make the trip he can't make. In his early conversations his mind wanders, and he contradicts himself. It's seems clear to the viewer that he is a man in serious trouble, although it is not clear early in the play what this is about.
As the play evolves we come to realize that the central issue in his life is his being caught with a "buyer" when Biff follows him to Boston to try to get Willy to help him with his failing Algebra grade. That moment changed everything in Biff's and Willy's lives. Biff's view of his Dad and his Dad's values is shattered, and Willy spends the rest of his life trying to regain the trust and love of his son. He ultimately ends his own life (generally considered an immoral act, although Willy's mental state certainly lessens his responsibility) in an attempt to get the insurance money that he thinks will kickstart Biff's career. That would make things alright between them. Sadly, since insurance companies don't pay on suicides, not even that is likely to happen.
In Miller's stage directions before Act One, he describes Willy as being more than sixty years old and "quietly dressed." His most obvious characteristic in this opening scene is his physical exhaustion, which remains a part of his character throughout the play. Willy describes himself as being "fat" and "very foolish to look at."
Willy's behavior is problematic as he slips further into depression and mental instability. He is subject to frequent and intense mood changes, and his temper flares easily. Emotional outbursts seem to come from nowhere, but they result from Willy's intense feelings of pain, fear, and frustration.As he deteriorates mentally, he slips in and out of reality, losing himself in memories of the past.
Willy is essentially a moral man. He feels responsibility for his family and worked hard to provide and maintain a home for his sons while they were growing up. After they grew up and left home, Willy continued to work hard to provide for Linda, struggling to pay off their house and other debts. When he was unfaithful in his marriage, the memory of it, and the pain it caused Biff, haunted him for the rest of his life. His guilt was deep.
Willy is motivated by the need to succeed; he defines himself and his value only in terms of financial success. As his career fades, he struggles against his sense of failure. At the end of Willy's life, he still pushes Biff to become a big success, just as he had always pushed him, in an attempt to "save" Biff from failure and, therefore, save himself from his additional failure as Biff's father. Willy's suicide is motivated by his need for success and his sense of responsibility for his family. He kills himself to provide for them financially (insurance proceeds) and to show his sons, by way of his "big funeral," that he had been an important and successful man.