What is Hemingway trying to point out in "A Clean, Well-Lighted Place"?
Hemingway is pointing out that life is relativistic and existential, in other words, meaningless and empty with no purpose. Notwithstanding, this philosophical perspective may not actually be true. The relativistic philosophy of existentialism has faded and been replaced with efforts to find and substantiate a meaningfulness in life that existentialism stripped from experience. Some of this effort to find meaning in a post-relativistic and post-existential milieu is seen in the surge of conversion to Buddhism and Judaism. Nonetheless, the point that Hemingway was making in the midst of an upsurge in relativistic existential ideology is that life is meaningless and without purpose. It is empty. It is nada.
It was all a nothing and a man was a nothing too. ... Some lived in it and never felt it, but he knew it all was nada y pues nada y nada y pues nada.
Nada is a Spanish word that is translated as nothing. Hemingway is saying life is an empty nothing that must be improved by light and a "certain cleanness and order":
It was the light of course, but it is necessary that the place be clean and pleasant. ... light was all it needed and a certain cleanness and order.
This understanding of Hemingway's point is confirmed in the exposition (the opening) of the story in which the waiter tells the younger waiter that the customer had "[last] week ... tried to commit suicide" because he "was in despair" about "nothing" ... about nada.