"Stepping into other people's shoes" is a figure of speech for putting oneself in the place of others in order to understand their attitudes and actions better.
Here are further instances of this altruistic act:
Miss Maudie answers questions from the inquisitive Scout, who wonders about the mysterious recluse Arthur (Boo) Radley. Miss Maudie states that he "just stays in his house, that's all....Wouldn't you stay in the house if you didn't want to come out?" However, Scout does not understand, contending that she would want to come out and wondering why Boo does not. Miss Maudie then reminds her of the history of the Radley family so that Scout can be understanding of Arthur by "walking in his shoes."
After Jem makes a snowman that too strongly resembles Mr. Avery, Atticus reprimands him for making "caricatures of the neighbors." Jem sees nothing wrong with the resemblance, but Atticus replies that Mr. Avery may not think so. For Mr. Avery, who has blamed the snow on the children--"It's bad children like you makes the seasons change"--may feel Jem's snowman is a retaliation for that remark. Jem needs to consider the man's feelings; in other words, "walk in his shoes."
After Jem tears the blooms from Mrs. Dubose's camellias, Atticus has his son read to her at her house. In fulfillment of this assignment, Atticus hopes that Jem can "walk in the shoes" of Mrs. Dubose and realize how terribly ill the elderly lady is. Perhaps, then, he will gain an understanding that she cannot be held responsible for all that she says. Later, Atticus reveals that Mrs. Dubose has been addicted to morphine so she has not been in control of her mind. But she bravely withdraws from the morphine before she dies, and she has a peace offering of a single white camellia sent to Jem.
There are several examples of Jem and Scout taking Atticus's advice to
"...climb into his skin and walk around in it" (Chapter 3)
before judging other people's actions. It is a repeating act that reflects the theme of tolerance in the novel. Sadly, most of the people of Maycomb do not practice Atticus's words. Presumably, Scout decides to do so before returning to school the next day and dealing with Miss Caroline again. At the end of the novel, Scout steps into Boo's shoes and gazes out upon her neighborhood, seeing things as Boo saw them for the past two years.
Atticus was right. One day 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 also suggests that Jem stand in Bob Ewell's shoes in order to understand his hatred for Atticus.
"I destroyed his last shred of dignity... the man had to have some sort of comeback..." (Chapter 23)
Sheriff Heck Tate utilizes Atticus's advice when he steps into Boo's shoes before deciding to call Bob Ewell's death self-inflicted.
"... taking the one man who's done you and this town a great service an' draggin' him and his shy ways into the limelight--to me, that's a sin." (Chapter 30)