Atticus' advice to Scout comes after her disastrous first day at school. Her father tells her 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."
Atticus suggests that Scout apply this advice to both Miss Caroline, who has punished Scout and insulted him; and to Walter Cunningham Jr., to whom Scout was unknowingly rude. Later, Scout uses this advice to better understand the actions of Bob and Mayella Ewell, as well as her Aunt Alexandra when she tries to emulate her actions after Atticus has broken the news about Tom Robinson's death. She is impressed with her aunt, who composes herself and returns to her duty of passing out refreshments to the Missionary Circle.
After all, if Aunty could be a lady at a time like this, so could I.
The best example comes at the end of the story, when Scout literally stands on the Radley porch in the same spot that Boo must have stood when he looked out over the neighborhood at night. Seeing things from his viewpoint, she envisions a side of the neighborhood she had never understood.