There is great thematic significance in Willy's job. The play illustrates the bewitching yet destructive force of the American Dream, and Willy's identity issues and lack of success are enmeshed in the dream and the demands on a salesman.
Willy is not a 'natural' salesman, he is 'foolish to look at, old, exhausted and delusional. Willy is driven by the image of Dave Singleman, a supremely successful and popular salesman, whose demise gives us the title of the play. It is as if Willy's whole life has been directed to him achieving popularity - he is so desparate for recognition but can see it happening only after his death.
We learn through Willy's flashbacks that he has never been successful. He missed out on the opportunity to make his fortune like his brother, Ben, and still calls upon his long-absent brother for advice. He cannot see that the wealth he has is his family. He does not even hear when Ben tells him this-
BEN:William, you're being first-rate with your boys.
We are never told what Willy is supposed to sell, and this is an irrelevant detail. What Willy was supposed to sell was himself, but this was never Willy's strength. As Biff says in the Requiem-
BIFF: He had the wrong dreams, all wrong.
Willy was good with his hands: he had done lots of work on his house. He was more suited to creating and making rather than selling. Charley tries to explain the purpose of a salesman, and it is here we realise just how mismatched Willy and his career were-
CHARLEY:...He don't put a bolt to a nut, he don't tell you the law or give you medicine. He's a man way out there in the blue, riding on a smile and a shoeshine. And when they start not smiling back-that's an earthquake.
Willy had faced the earthquake much earlier in his career but, trapped by consumerism, debt and ambition, Willy is condemned to follow his path to his death.