The narrator's epiphany near the end of "Cathedral" is one seeing the world from a new perspective. Throughout the short story, Robert is characterized as a self-obsessed, ego-centric personality who only sees people and events from his own point of view; we see this in his actions and his speech from the very opening lines of the story. He never takes the time or makes an effort to see anyone or anything from another point of view; he sees no purpose or value in the activity. Robert's visit changes all this--at least momentarily--for the narrator. Through helping Robert to draw and be able to "see" the Cathedral, the narrator has an almost religious experience of his own, finally realizing the value of seeing people and things from multiple points of view.
In the story "The Cathedral," the narrator's wife has a visitor coming to stay for a short time, a blind man named Robert who the narrator's wife used to read for.
She has not seen Robert since her divorce and remarriage to the narrator, but Robert has since lost his wife, to whom he was very close.
The narrator has no sympathy for the blind man, behaving abominably toward their guest, much to his wife's dismay. When the narrator's wife retires for the evening, the narrator and Robert stay up, while the narrator thoughtlessly watches the television, trying to relay the images to Robert who, of course, cannot see them.
When a program comes on and describes a cathedral, the narrator struggles to describe what he sees with mere words. At this point Robert asks the narrator to get paper and a pencil in order to draw the cathedral, and the narrator complies. Then Robert tells the narrator to start to draw, while Robert's hand rests upon the narrator's. With encouragement from Robert, the narrator starts to sketch.
Then Robert tells the narrator to close his eyes and continue to draw. As he does so, the narrator notes something extraordinary happening to him. His short moment of "blindness" has allowed the narrator to "see" what he could not "see" before. Robert tells the narrator he can open his eyes, but still he does not.
By closing his eyes, the narrator, knowing the physical boundaries of the rooms, of his home, feels that there are no boundaries at all. He is somehow freed from his preconceived notions of his wife's friend, the man's blindness, and what he has perceived up until now as his own superiority in the order of things. His hostility and jealousy toward Robert vanish, the sense of separation he felt from Robert because of Robert's infirmity disappears, and the narrator senses that something new has awakened within him and that he will be able to be a different person with this new "insight" he has of the world and his place in it. He is a fortunate man to have been given the chance to see the world from a different perspective and chose to use this experience to change himself.
This is the epiphany the narrator experiences at the end of the story.