One significant symbol in this story is the "shadow of leaves," a phrase repeated in three descriptive passages. The dominant theme is the existential nothingness, the "nada," of life; the meaningless in which each individual must create their own meaning. The old waiter says the "shadow of leaves" are an advantage to those who want "a clean, well-lighted place" to sit in when they don't want to sleep, when they "need a light for the night."
The well-lighted cafe creates an appearance of a life with substance, a life not completely overshadowed by the darkness of "nada" (i.e., "nothing"). The shadow of leaves creates an illusion of substance; an illusion of a something dancing in the nothingness. This appearance of substance is comforting for those who have no hope left for meaningfulness, who have come to despair in an existence of meaninglessness: they have come to what is called existential despair.
The "shadow of leaves" is the symbol of this appearance of substance, this shadow of substance that counters the nothingness of a meaningless existence. In other words, if life has no meaning to it, if the universe is in fact meaningless and despair (i.e., hopelessness) is the end of all humankind, then pick something that offers the shadow of light, of beauty, of interest, of hope to latch onto to in the surrounding darkness that is teeming with despair, as represented by the girl and soldier on a street quiet with dew and one street light.
This is a clean and pleasant cafe. It is well lighted. The light is very good and also, now, there are shadows of the leaves.
the tables were all empty except where the old man sat in the shadow of the leaves of the tree that moved slightly in the wind. A girl and a soldier went by in the street. The street light shone on the brass number on his collar.
A possible sample thesis statement (depending upon your level of writing development) might be something like: Since Hemingway is exploring the alternatives to a life of dark nothingness, the symbol of the "shadow of leaves" illustrates that he believes any alternative will be the allusion of substance and not substance itself.
Alternatively: Since Hemingway is exploring the alternatives to a life of dark nothingness, the symbol of the "shadow of leaves" illustrates that the older waiter believes any alternative that is the mere allusion of substance and not substance itself is as important as real substance.