Empathy implies that you understand and relate to what a person is going through, because you have gone through it yourself. In "Cathedral", the main narrator finally is able to develop empathy for the blind man, Robert, because he closes his eyes and experiences something as the blind man would. Before this incident, he is a rather callous, bitter, unhappy and insensitive man. But then, the bllnd Robert has him close his eyes and attempt to draw a cathedral. The experience is completely profound for the narrator; he finally understands something from someone else's shoes, and therefore has empathy. It is so moving for him that he says of it, "It was like nothing else in my life up to now." For the rather understated narrator, that statement says a lot.
In "To Kill a Mockingbird," empathy is found in many, many different characters, and is just an overall theme. Harper Lee writes a story that helps us to feel for a black man's hopeless situation, and to feel for an anti-social man who is misunderstood in society. We even can feel a little bit for the controversial Mayella Ewell, as we get a closer glimpse of her pretty depressing home life. Even old, surly Mrs. Dubose is seen in a kinder light as we discover her attempts to overcome addiction before her death. Harper Lee likes to take what seem to be, on the surface, unlikable people or characters, and help us to develop a bit of empathy for them as we see their human sides.
I hope that those thoughts help to get you started; good luck on the essay!