Why do the men listen to the music?
There is an implicit contrast throughout the story between the present and the past. The four men are living in the wasteland created by a great nuclear war. Although the bombs did not kill everyone, the radioactivity eventually accounted for most of the survivors, and the poisonous clouds cut off so much sunlight that most of the vegetation died off.
...there was no structure or remnant of a structure visible over the dome of the darkling earth, but only, in sheltered hollows, the darker shadows of young trees trying again.
The four surviving men are evidently living out on the prairie in what used to be the United States. They realize, and also symbolize, how foolish it was for intelligent human beings to destroy everything it had taken thousands of years to create. The four books and the dozen classic phonograph records symbolize the marvelous civilization that had existed throughout much of the world before someone pressed a button and delivered the first bomb. The men listen to the music because it helps them to remember what things were like before the atomic holocaust. It is all they have to do, and all they have to live for. It helps them to escape from their present unbearable condition.
"Still," said the man who had admired the books,"we need the absolute if we are to keep a grasp on anything....Anything but these sticks and peat clods and rabbit snares," he said bitterly."
The music by Debussy is appropriate because it is peaceful and civilized. It was music to be played in comfortable salons where food and wine were plentiful and everyone wore immaculate clothing.
At the first notes of the piano, the listeners were startled. They stared at each other. Even the musician lifted his head in amazement, but then quickly bowed it again, strainingly, as if he were suffering from a pain he might not be able to endure.
The moral of the story is obvious from beginning to end. "This is what could happen if men don't come to their senses."
The men agree to hear Debussy’s Nocturne for piano, primarily because the musician (paragraph 44), whom they regard as an expert, selects it. The playing time of this piece, which is less well-known than Debussy’s three Nocturnes for orchestra and chorus, is about six minutes, although on old seventy-eight records this time would necessarily have been reduced. Reactions of the listening men are described in paragraph 45. Three of the men perceive "tragically heightened recollection" while the musician listens more objectively, hearing "nothing" but what is there. His response when the music ends indicates his heightened emotion and therefore his appreciation.