Given Hemingway's general view of life, which is relatively grim at best, the story gives us a consistent, if equally grim, discussion of how one copes with life.
The three characters--the young waiter, the old waiter, and the old man--cope with their lives in different ways: the young waiter, who has his whole life ahead of him, looks forward to ending his shift, closing the bar, and getting back to his wife and family; the old waiter doesn't seem interested in doing anything accept treating his old customer with respect and decency; the old man, who recently tried and failed to commit suicide, is simply interested in getting quietly drunk in a pleasant setting.
The juxtaposition of youth and age, however, is not the essential conflict in the story. The two older characters, who have lived their lives and have not much to look forward to, conclude that their time is up in this world--their way of coping with what is left of their lives is characterized by fatalism, that is, a view that because death is inevitable, nothing that one does matters.
What does matter, though, is the choice of how and where to spend one's remaining time. Because dim, dark bodegas simply remind the old man how close he is to death, he chooses instead a place that is well-ordered, quiet, clean, dignified--those things that represent life to him. Of course, getting quietly drunk is another way of coping with the reality of mortality and death because it provides temporary oblivion to those things.
The old waiter, like the old man, acknowledges his own mortality when he says that life essentially consists of "nada y pues nada y pues nada" (nothing and then nothing and then nothing), a perfect epitaph for the two old men who see nothing before them except "nada."