What does cathedral mean in the story?
The cathedral could symbolize change. As the narrator draws the cathedral he finds that he is unable to draw it correctly. When Robert tells the narrator to try to draw it with his eyes closed, he finds that he is able to draw more freely. This drawing of the cathedral changes the narrator's attitude toward Robert. He is able to make a connection with Robert and he is not as afraid or judgemental of him.
The narrator also becomes enlightened by drawin the cathedral because he realizes that he has never really made a connection to anyone before, not even his wife. He doesn't want to open his eyes at the end because he is afraid of losing the connection the cathedral has brought to him.