What does Scout learn, and how does she change in the course of her narrative?
To Kill A Mockingbird is narrated by an adult Scout, whose entire narrative is a reflection of the events that took place during her childhood in Maycomb. As the novel opens, Scout is 6 years old; she, Jem, and Dill spend most of their days attempting to communicate with Boo Radley, the neighborhood recluse. As the children are young and relatively insensitive to boundaries, their behavior borders on harassment; they try to look into the Radley windows, enact plays in which the children pretend to be members of the Radley family, and even try to put notes into the Radleys' house by attaching them to a fishing-pole. Repeatedly, Atticus warns the children to leave the Radley's alone, telling them that the Radleys have a right to live their lives in peace and "free from the attentions of inquisitive children." Despite these warnings, the children continue with their quest to see Boo Radley and fail to understand the harm in their actions.
Also in Part 1 of the novel, Atticus tells Scout that "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." This, perhaps, is Atticus's most important advice. Though in that instance, Atticus is referring to Scout's teaching, Miss Caroline (she's new to the area and to teaching, and Scout is upset because Miss Caroline doesn't understand Maycomb's ways or citizens). However, Atticus tells Scout this advice in the hopes that she'll apply it to every experience she has.
Part 2 of the novel centers around the Tom Robinson trial, and as she is allowed to watch the proceedings, Scout gradually recognizes that Tom is an innocent, respectable man whose life has been put on the line to cover up the Ewell family's lie. Though Scout isn't as affected by the trial as her older brother is, she does see the injustice that's present in her society.
At the end of the novel, when the Finch children are attacked by Bob Ewell and consequently saved by Boo Radley, Scout is finally able to put herself in someone else's shoes--in this case, Boo Radley's. After she walks him home, she stands on his front porch and observes the neighborhood from his perspective. Doing so allows her to see things as Boo has seen them for so many years, and she is finally able to see the value in Atticus's teachings. And at the end of the novel, as a result of the experiences that she describes in her narrative, Scout is a more mature, more tolerant, and more understanding young lady than she was at the beginning.