In Raymond Carver's "Cathedral," the church building symbolizes vision to the narrator. Vision is...
...an experience in which a [person], thing, or event appears vividly or credibly to the mind, although not actually present.
The blind man's eyes do not "work," but he "sees" so much more than the narrator whose sight is not impaired—though his perceptions of the world seem to be. The narrator has a limited understanding of the world: he makes judgments based on what he sees. Robert, the blind man, bases his perceptions on what he feels within: he may not see the cathedral, but to him it symbolizes learning—its grandeur is not what makes it important, but the work of countless men who lived and died to build the structure without ever having the satisfaction of seeing it completed in their lifetime.
The narrator lets his jealousy of the platonic relationship his wife shares with Robert, over many years of acquaintance and the death of his wife, interfere with the narrator's ability to behave like an adult. As they prepare for Robert's arrival, the narrator 'snidely suggests how he might entertain the man.
Maybe I could take him bowling...
His wife makes it clear that if their relationship means anything to him, he will be nice to this man who is not only her friend, but who has recently lost his wife.
Their conversation provides indirect characterization: when he notes he has no blind friends, his wife points out he has no friends at all. We learn that he is a shallow individual. When he behaves ignorantly again, she begins to lose patience with him:
She'd told me a little about the blind man's wife. Her name was Beulah. Beulah! That's a name for a colored woman.
"Was his wife a Negro?" I asked.
"Are you crazy?" my wife said. "Have you just flipped or something?...What's wrong with you?" she said. "Are you drunk?"
His tendency to generalize can be seen in his question about Robert's dead wife: that Beulah was "a name for a colored woman." By the time Robert arrives, the narrator has shown how insensitive he is; his wife is disgusted with him.
As the evening progresses, the narrator learns that what he thought he knew of the blind (very little) is untrue: he'd heard they didn't smoke because they could not see the smoke they exhaled—Robert smokes...a lot. Robert decides to "watch" TV with the narrator, who says he is happy to have the company...and means it—showing a subtle shift in his character. The program is about cathedrals, and he asks Robert what he knows about them. Robert says:
I know generations of the same families worked on a cathedral...The men who began their life's work on them, they never lived to see the completion of their work...they're no different from the rest of us, right?
It is not a surprise when the host admits he believes in nothing. Then Robert asks him to draw a cathedral—eyes opened at first and then closed—while Robert follows the movement of his hand. The host is transported. Robert asks him to look, but he hesitates, and...
I didn't feel like I was inside anything.
The narrator has an epiphany—"a sudden intuitive realization." He understands the world without sight. It changes his sense of what he thinks he knows—no longer judging by appearance or preconceptions, but experiencing the world through his "mind's eye." A cathedral is awe-inspiring visually, but the host is inspired because he "feels" it, and so, knows it as well.