Atticus's first lesson about tolerance of others revolves around the above quote. It comes after Scout's disastrous first day at school when she is chastised and then punished unfairly by her new teacher, Miss Caroline. Atticus explains to his daughter that both she and the teacher had "learned things today." Miss Caroline learned about the ways of the Cunninghams,
... but if Walter and I had put ourselves in her shoes we'd have seen that it was an honest mistake on her part. We could not expect her to learn all of Maycomb's ways in one day, and we could not hold her responsible when she knew no better. (Chapter 3)
Atticus later tells Jem to "stand in Bob Ewell's shoes a minute" to understand why the man has such a strong hatred for Atticus. At the end of the novel, Scout looks out from the Radley porch, standing in Boo's shoes and imagining that she is seeing things from Boo's perspective.
Atticus was right. One time he said you never really know a man until you stand in his shoes and walk around in them. Just standing on the Radley porch was enough. (Chapter 31)
Atticus's advice simply means that one's opinion of others may not always be accurate, especially upon first impression; by first stopping to consider things from the opposing point of view, one might better understand another person's actions and reasoning.