Why does the blind man tell the narrator to close his eyes while he is drawing? What does he hope to teach him? What is the narrator able to “see” with his eyes shut that he cannot see with them open?

The blind man, Robert, is teaching the narrator how to connect to himself and by extension other people. From the beginning, the narrator is consumed with jealousy and other negative feelings that prevent him from giving himself to others and from allowing other people to give to him. At one point, for example, his wife tells him, "You don't have any friends," and the reader can see exactly why. While Robert and the narrator's wife talk, the narrator stays on the peripheral of the conversation, only adding the odd comment because he "didn't want him to think [he'd] left the room."
The turning point of the story comes when the narrator decides to offer to smoke some dope with Robert. He states that he mostly smoked by himself at night, staying up to watch TV while his wife was sleeping. This time he knows that the blind man is going nowhere. He has to connect with him somehow, and the only way he can think of is by smoking weed.
Finally, the narrator gets out of his own mind and begins to take an interest in the blind man. After all, it is the narrator who brings up the subject of cathedrals. He states, however, that he only knows what cathedrals look like from TV. As if TV is his only real connection with the outside world.
Robert teaches him that he instinctively knows what Cathedrals look like. If he just closes his eyes, relinquishes control, and connects with his memories, he can reach out to whatever and whoever he wants.
As the narrator states at the end of the story:

My eyes were still closed. I was in my house. I knew that. But I didn’tfeel like I was inside anything.