Magical realism is a literary style, especially popular in much Latin American literature, which combines the everyday details of realism with elements of fantasy and magic. The weaving of the everyday with the fantastical is what creates the distinct magical realism style. Unlike fairy tales and fables, these are not clear moral tales, nor do they seem "other-worldly" as fairy tales do. Rather, they seem much more ordinary--as if the magical occurrences were the most expected thing in the world. The reader needs to work to find the meaning and intention within the tapestry of magical and realistic occurrences.
"A Very Old Man with Enormous Wings" tells a tale of what happens to a seemingly ordinary town when an angel appears. An essential point in the story is that the angel isn't at all what the people expect of an angel: he's a disappointment. When he arrives, only his wings cause him to appear to be anything but a rather ordinary old man. Pelayo and his wife Elisendo, who discover him, conclude he's a sailor, but their neighbor tells them with assurance that he's an angel. (There's the magic--the wings; the realism is in the ordinary quality of his appearance and the way the couple discusses him.) The middle section of the story describes all the ways in which people abuse the angel, probably because he is not what they expect of an angel--and possibly because of what he doesn't do for them. Later a spider-woman appears, as magical and supernatural as everyone had at first hoped the angel would be. She appeals to crowds in ways that the angel could not. She fits the mold of what people expect of a supernatural being; even miracles performed by the angel fall short of the crowd's expectatations.
Pelayo and Elisendo, now wealthy, continue to keep the old man about, but his health deteriorates and he is considered a nuisance until the end of the story, when he finally is able to use his wings, and he departs. This is many years after his arrival; his departure is seen as a relief.
Of course, the magical elements are the wings (deemed "logical" by a doctor), the angelic miracles, the spider-woman, and the spider-woman's miracles, but all of this is set amidst the ordinary. People do not see the miracles and the goodness that is closest to them.