In paragraph 96, the blind man observes that the men who began work on a cathedral never lived to see it completed. In this way, he says, “they’re no different from the rest of us.” What does the cathedral symbolize to the blind man? What does it come to symbolize to the narrator?

An interesting question. Certainly, this story is full of symbolism and dual meaning—what is seeing, really? How is it that the sighted man believes himself superior to the blind man throughout the story, but then, at the end, finds out that he doesn't know any more than the blind man does about what a cathedral really is?
We could argue that the cathedral represents purpose, or the truth of what we are really doing with our lives. To the people who built it, pious people in the Middle Ages, they knew that the cathedral represented a monument to the God they believed in, but did they really understand what that God represented? They were listening to masses performed in Latin and which were not explained to them; they spent generations working towards the goal of this cathedral which would memorialize that God, but they would never see the sum of their works, or ever really understand the truth of what their God really was. The cathedral to them, then, is a symbol of an immortal truth into which they put their faith without really knowing much about it.
In the same way, it seems that the cathedral to the blind man, as well as to the narrator, symbolizes what they do not know; what are they really working towards? The sighted man thinks he knows more than the blind man, but earlier in the story he has admitted that he doesn't like his job and doesn't know what else he could do. He doesn't know what his purpose is in life. Meanwhile, the blind man has been unable to see his own wife, which the narrator thought was "pathetic," but at the end of the story, he acquires a new realization of what true sight really is.
Together, the narrator and the blind man draw the cathedral, both of them without the use of their eyes, and with the blind man's encouragement, the narrator finds that he does know, really, what a cathedral is; he knows more about it in greater detail than he realized. What is represented on the page, then, is the truth of what the narrator knows about life and his purpose; he is able to discover more about himself without his sight than he was able to through the use of his eyes.