Willy Loman is a failed dreamer. He is a failure because he cannot or will not let go of the false dream he clings to. If Willy were to wake up to reality, he would see that he is not a complete failure in life. Yet his only real failure is his inability to do this, to face reality.
Willy is a salesman, a husband and a father. He has made mistakes in all three of these identifying categories. We can call these "social categories", reflective of Willy's social persona.
Willy's sales methods have fallen out of favor. At the height of his (relative) success, he is caught cheating on his wife by his oldest son. He then kicks Biff out of the house, failing to explain or even apologize for what Biff has seen.
There are counter-points to these failures. Willy and Linda are set to make the final payment on their mortgage and will soon own their home outright. This is an achievement. Critically, this is a success directly related to the general conception of the American Dream.
As a home owner, Willy has reached a position of success regarding the American Dream. Due to his fixation on the kind of success defined by his brother Ben, Willy can only see himself as a failure. He seems to be oblivious to his modest but significant success. His American Dream is for greatness, nothing less.
Many critics have asserted that Willy is a modern tragic hero, and that his tragedy lies in his belief in an illusory American Dream.
Emotionally, Willy is childish, sensitive and weak.
Willy is highly emotional, unstable, uncertain at times, highly contradictory, and seems worn down by life.
Psychologically, Willy is highly unstable as we see him in the play. Not only is he fixated on a delusion regarding his own potential, he also hallucinates and talks to people who are not present. Flashbacks overtake him and he has no power to control where his mind goes; no ability to stick to reality.
The stress derived from Willy's ambition to be great and his failure to do so leads Willy to ignore his talents, falter as a father and husband, and finally to despair of his human value.
Willy struggles with the image of his ideal self his entire life, until he can no longer deny the fact that he will never become this ideal self and he commits suicide.
Miller presents and explores the character of Willy through a variety of means. All the other characters in the play speak about Willy, offering their own analysis of his motivations, his weaknesses and his humanity. Willy is also given opportunities to articulate himself as he talks with his brother Ben, defining his vision for himself, and as he talks with Charley, Linda and Biff about the nature of success.