How does Harper Lee convey the themes of the narrative? What do we learn when characters demonstrate the act of seeing from another's perspective?

One theme in To Kill a Mockingbird is compassion. Early in the book, Scout had a hard day at school when she expected her teacher, Miss Caroline, to understand the routines of the townspeople (such as the Cunningham family and the Ewell family). Atticus gives advice to Scout:

"if you can learn a simple trick, Scout, you'll get along a lot better with all kinds of folks. You never really understand a person until you consider things from his point of view . . . until you climb into his skin and walk around in it." (ch. 3)

Throughout the novel, Scout and Jem are put into multiple situations where they have to consider another person's feelings or point of view. When Scout and Jem choose to see life from another person's perspective, they generally learn to feel compassion.
For example, Jem grows in compassion for Boo Radley when Jem recognizes that Mr. Radley (Boo's father) filled in the tree hole that Boo was leaving gifts for the children in. Jem isn't sad because he can no longer receive gifts; he's sad because he realizes that Boo is kept entirely separated from the rest of the world. He learns to see the world through Boo Radley's perspective, and he feels compassion for him.
Later, Scout feels compassion for Mayella Ewell. She explains,

"As Tom Robinson gave his testimony, it came to me that Mayella Ewell must have been the loneliest person in the world. She was even lonelier than Boo Radley, who had not been out of the house in twenty-five years." (ch. 19)

Here, Scout begins to see life through Mayella Ewell's eyes. She realizes that Mayella had no mother to care for her, that she had many siblings who depended on her, and that she had no friends in the community. Scout puts herself in Mayella's shoes, as Atticus suggested, and she feels compassion for her misfortunes. These are just two of many examples where the Finch children learn to see life from another person's perspective.