In Death of a Salesman, what is the importance of "being liked" in the play?
The idea that being popular is important is the philosophy by which Willy lived his life and conducted his career as a salesman, and the one he passed on to his sons, unfortunately. Willy believed that a man succeeds by making a good appearance and winning friends with his smile and personality. These misconceptions Willy drills into Biff and Happy all their lives, even at the end of his own life when his sons' lack of success can no longer denied.
Willy's conversation with the adult Bernard shows that he really does not understand how Bernard had succeeded whereas Biff had failed. In Willy's thinking, Bernard's great success is impossible to understand since as a boy he was always so unpopular and wasted so much time studying instead of playing sports to make people admire him. Willy asks Bernard directly about his success: "What's the secret?" Because of his skewed belief, Willy cannot see the relationship between education and success (Bernard), between risk-taking and success (Ben), or between business innovation and forward-thinking (Charley). Instead, success remains elusive for Willy even in his last hours. He plants vegetable seeds in a garden that will never see the sun. Even in this, Willy cannot see the relationship between cause and effect.
Willy kills himself to gain the proceeds of his life insurance for his family, but he contemplates even his own death in terms of his popularity:
[My] funeral will be massive! They'll come from Maine, Massachusetts, Vermont, New Hampshire! All the old-timers with the strange license plates . . . . Rhode Island, New York, New Jersey--I am known . . . .
In one of the play's final ironies, Willy's funeral is not well attended.
For Willy, it's the most important thing in the business world. Willy lives in an old world, a world where business was done on a handshake, where friends were part of the way things "got done." He tells his sons over and over that this is the way to get ahead; in contrast he predicts that Bernard, despite the fact that he is very intelligent and performs much better in school than Biff, will amount to nothing because he has no personal attractiveness. He finds out later that none of this makes any sense in the new world of business. Bernard is a lawyer, about to argue a case before the Supreme Court; Biff has just gotten out of jail, and there is no indication that he is going to amount to much in the business world ... or that he even cares, although his not caring may be the result of his previous failures?
In the modern world that Willy inhabits, but isn't a part of, a man IS a piece of fruit, you can eat the fruit and throw away the peel, and that how you perform is the true measure of your worth, not whether you are "well liked."