The author is not explicit about what the old man with wings represents, so a reader can have a fair amount of latitude with this question. Personally, I have always liked to emphasize the fact that the old man has wings. That is shocking and amazing and awe-inspiring. It should immediately call to the mind images of heaven and heavenly creatures. It is miraculous; however, that is not the only response of the people to the fact that this old man has wings. Take the doctor that examines the old man as an example. The doctor notes how the wings fit the old man's body. They are not some kind of tacked-on addition. The doctor's response is that the wings appear entirely natural, and he wonders why other people don't have wings. The old man essentially appears so normal with wings that people without are the oddity.

Other descriptions take away the amazing qualities of the wings, too. They are "buzzard wings" and "strewn with parasites." They are "dirty and half-plucked." There is nothing angelic about their descriptions, and this creates an interesting blend of the sacred and the mundane. The man is both beautiful and pitiful at the same time. He is a miracle, yet he is normal, and I believe that is the symbolic key to the man. People of all belief systems like to consider the possibility of miracles, and I think they tend to believe that miracles should be huge, loud, beautiful, and unmissable. They fail to realize that miracles are not necessarily something out of the ordinary. They can be tied to everyday life. Take the human heart as an example. On average it beats seventy-two times per minute. It does this minute after minute, hour after hour, day after day, and it does this for decades. Humans have yet to build a machine that works so well for so long with so little maintenance. It's an everyday miracle, just like the old man.

The very old man with enormous wings never speaks—we only learn that he doesn't seem to understand Latin—and we learn nothing about him except for an external description: he is old, he has wings, he smells bad, and his feathers are messy and infested with parasites. Who he is, where he came from, and what he wants are all unanswered questions. What he represents is the new and unusual—the extraordinary—descending into ordinary life and the human indifference to this gift.

What is important about this figure is how the people and society around him react to his presence. He raises the suspicions of the local authority—the priest—because of his odors and infestations. He does not seem pure and otherworldly enough to meet the priest's preconceived notions of what an angel should be. Yet his wings preclude him being treated as an ordinary human.

We see the institutional power of the Catholic Church in Rome paralyzed and unable to deal with this figure, unwilling to provide guidance. Local people, such as Pelayo and Elisenda, treat him as a piece of property and commodify him. They charge people to see him and use the earnings to build themselves a big house. The people who come to see him treat him as an "other," an object to gawk at because he is different from them.

The old man with wings represents the inadequacy of the human response to the new and potentially wonderful and the way we reject the gifts of the "other." Rather than try to know and understand him, the human world reacts by turning away away from this winged creature (as the church does by dragging its feet) or by crude exploitation. Society markedly does not respond to him compassionately or empathetically. Elisenda, for example, is relieved when he flies off and is no longer an "annoyance" in her life.

"A Very Old Man with Enormous Wings" plays heavily on ambiguity.

Garcia Marquez never allows the reader to settle comfortably into one attitude or the other...

For this reason, identifying a single meaning in the winged character is quite difficult. A number of symbolic meanings are available depending on our interpretation. 

The most compelling reading of this character sees him as a representative of people's faith, both in humanity and religion. Like religion in the context of the story, the man is open to interpretation. Also, religion in the text is represented wholly by humans and functions as an optional moral guide, to be chosen or cast away according to whim. 

...the villagers' magical beliefs are in fact ridiculous delusions; but at other times, the reader seems expected to take logically impossible events at face value.

Though the man is seen initially by some as an angel, he disappoints the set ideas that people have about angels. He is far from majestic.  He is instead more like ''a senile vulture'' or a ''decrepit hen.''

Instead of presenting a majestic, awe-inspiring figure, Garcia Marquez describes a creature with mortal weaknesses and senility...

The man is treated like an animal because he is seen as an animal. We can take this as a comment on the villagers views of humanity. As the man has failed to meet their expectations, the man is relagated to a coop, ridiculed and debased.

He is, then, a projection. He is what the people believe him to be. He is an avatar of perspective and belief. To go futher than this in our interpretation is to undermine the power of the ambiguity at the heart of the story.

The man is and isn't an angel. He is and isn't "just a man".