The blind man, Robert, could be said to represent the narrator's (husband's) prejudices. Prejudice, after all, is a kind of blindness. If I think that you are stupid because you are Polish, or a violent criminal because you are black, then I am "blind" to the real you.
At the beginning of the story, the husband has a number of misconceptions about blind people, including:
a) "the blind moved slowly and never laughed";
b) a blind man would probably not have a beard ("A beard on a blind man! Too much, I say.");
c) blind people don't smoke.
As the story continues, the husband discovers that Robert is not just a "blind man"; he is a unique human being, one who happens to laugh, smoke and wear a beard.
At the end, the husband tries to help the blind man understand what a cathedral is. The blind man holds the husband's hand as he draws a cathedral.
The cathedral represents holiness and beauty. The husband's friendship with the blind man, and his newfound openness to someone who is different, are beautiful and holy.
As the story closes, the husband closes his eyes, and keeps them closed. This could symbolize that really it was he, not Robert, who had been "blind" all along.