The answer above has the names wrong. It is Howard who is the son of Willy's original boss (whose name is Frank), not Charlie.
Charlie is Willy's next-door neighbor. He has real sympathy for what Willy is going through, and he has been regularly lending Willy money for years. Willy, of course, says that he will pay Charlie back, but he never will. They both know this.
Willy is embarrased by the position he is in vis-a-vis Charlie. Charlie is a succesful businessman and Willy is exhausted and losing it. He cannot take Charlie up on his job offer because of his embarrassment, his pride, and what taking a job would mean to Willy's dwindling sense of self.