The almost biblical setting of "A Very Old Man with Enormous Wings" along with the personification of the world contributes to the preternatural and fairy-tale atmosphere, or mood, of the story. 

Suggestive of the narrative of Exodus 8 in the Old Testament in which a plague of frogs was sent after the pharaoh who refused to free the Israelites, Marquez's story opens with crabs crawling across his property and throughout the inside of his house. Other strange things occur in nature:

The world had been sad since Tuesday. Sea and sky were a single ash-gray thing and the sands of the beach, which on March night glimmered like powdered light, had become a stew of mud and rotten shellfish. The light was so weak at noon when Pelayo was coming back to the house after throwing away the crabs, it was hard for him to see what was moving and groaning in the rear of the courtyard.

In this bizarre atmosphere, there appears "a fallen body" that is indefinable. At first, he is repulsive to Pelayo and his wife, but after their baby becomes well, they feel "magnanimous"; they then decide to put him on a raft with provisions and set him free to deal with his fate. However, when they go outside, they find their neighbors tossing food and tidbits to him through the openings of the chicken coop in which he has been placed. As a result of the strange being's presence, other oddities appear, such as the woman who was turned into a spider. Their presence then contributes to a fairytale setting which in turn contributes to the wealth of Pelayo and his wife because crowds come to see the strange being. Later on, however, the old man becomes a nuisance to Elisenda as he moves from room to room in their house. Later, she sighs with relief as he departs.

This is such an interesting question, especially considering that Marquez's stories usually contain an indeterminate time and place.  A Very Old Man with Enormous Wings is no exception.  This is because Marquez uses a technique often referred to as "magical realism" which simply means that elements of magic and fairy tales are embedded within the same story as elements from our reality.  This usually creates an intense frustration for the reader who is unable to determine any type of moral to the story.  Likewise, this leads to the mood of confusion and frustration, even within the characters of the story.

 A Very Old Man with Enormous Wings contains characters with names that suggest a Spanish-speaking country, although no country is ever named.  In addition, we are told of times past and seem to be in the midst of a fairy tale world, but are given references to modern methods of transportation which seem to pinpoint the story to the twentieth century or later.  By not setting the story in a particular time or place, Marquez creates a timeless effect which nicely leads the reader to consider his story to be universal.