This quote is from Willy Loman as spoken to Howard Wagner, the supervisor (and son of Willy's previous supervisor) at the company for which Willy works. Following Linda's advice, Willy goes to his boss to ask him for a permanent position within the office so that he does not have to travel so much. He also asked for a salary position, as Willy had been living off commission but, since he was not selling, he was really able to make it thanks to the handouts of money that he would ask his neighbor and friend Charley for.
The words are also a reaction to what Howard had told Willy after a long time trying to divert the situation.
I don't want you representing us anymore. I've been meaning to tell you for a long time now
To which Willy reacts in dismay for several reasons. First, because Willy still abides by the old code of friendship. He believed that Howard Jr. should reserve a special place of reverence to Willy as he had known him since he was a child. Moreover, Willy still also abides by the old code of loyalty: if you are loyal to the company the company should be loyal to you and keep you as an employee. Not the case; finances were looking up and productivity is a must in the mid 1940's; Willy is a piece of the old school and he must be taken away.
Hence, when Willy says
you can't eat the orange and throw the peel away--a man is not a piece of fruit.
he reflects this old school mentality: that you cannot just use someone with whom you co-exist, work with, and share with year after year and then one good day turn around and get rid of that person as if he had never been there. It is no different than feeling like trash: you are no longer useful, so we will throw you out.
Willy did feel eaten from the inside out by the machinery of selling: he neglected his marriage because of it, he got into debt because of it, he worked his heart out because of it and now he is no longer "needed". Not only does this emasculates him in the eyes of his family, but also makes him feel quite betrayed by those for whom he feels that he had done so much for. Like a "piece of fruit" the company indeed consummed most of his life and, now that he has none that he could be proud of, they just decided to throw away his "peel" and get rid of him for good.