Insomnia in "A Clean, Well-Lighted Place" is indicative of the feeling of hopelessness or disillusion that the older waiter is feeling about life.
He dismisses this disillusion as "insomnia," but it represents more than that. The older waiter seems to be of the generation who saw the worst of The Great War (World War I) and dismisses this disillusion about life as this disorder and says "many must have it."
So how does the reader know that the older waiter suffers from disillusion, or nothingness? Two reasons:
- His empathy for the old man who tried to kill himself. As characters, the older waiter is much more like the old man than the younger waiter. The old man has no one except for a niece and his suicide attempt was a way for him to end his feelings of nothingness.
- The prayer. The older waiter replaces many words in "The Lord's Prayer" with the word "nada" (Spanish for "nothing"). This suggests that Catholicism and religion as a whole, which is what many used to replace a feeling of disillusion, no longer satiated people.
It's important to remember that diseases and disorders in fiction are chosen very carefully. Insomnia is very symbolic in that it prevents sleep, which is a way for people to shut out the bad things, at least for a little time. For the older waiter, the bad things can never be shut out.