This is a great question. Let me start off with a quote from Miller:
"I believe that the common man is as apt a subject for tragedy in its highest sense as kings were. On the face of it this ought to be obvious in the light of modern psychiatry, which bases its analysis upon classic formulations, such as the Oedipus and Orestes complexes, for instance, which were enacted by royal beings, but which apply to everyone in similar emotional situations."
Miller sought to make this statement a reality by his play, Death of a Salesman. He choose as his protagonist, Willy Loman, a traveling salesman. He had delusions of grandeur; but there were also glimpses of his failure as a person on many levels. He was a failure as a salesman, husband, and father. He cannot face these realities. So, he tries to keep up his illusion of success, but this wears out. He also tries at times to live vicarious through his sons, Biff and Happy, but this fails as well.
In the end, Willy sees no solution. So, he kills himself by crashing his car. Part of the reason for this was so that Biff would get the insurance money to start a business. The other reason was due to the fact that he could not face reality anymore.
Miller's point in writing a tragedy for the common man is simple. If common people can appreciate tragedy, then they can become tragic as well. He successfully shows this in Death of a Salesman.