How is the idea of walking around in someone else's skin meaningful in To Kill a Mockingbird? I also need cited examples from the book.
This is a very important concept in the book and serves as one of the central themes. Atticus is trying to teach Scout and Jem to consider things from other people's perspectives. This is an important lesson for them, as maturity takes place when people are able to see things from the vantage point of another person.
In chapter three of the book, Atticus gives these words to Scout to help her in school.
“First of all,” he said, “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.”
As the novel progresses, both Jem and Scout are better at doing this, and so they mature. For example, in chapter seven, Scout says that she tried to walk around in Jem's skin for awhile.
As the trial progresses, Jem and Scout are able (to a certain degree) to see things from Tom's perspective. The text is not explicit, but we can deduce this from their desire to see Tom free.
In the end, Scout is able to see things from Boo Radley's point of view. In fact, she learns this lesson so well that she is more insightful than Atticus in some ways. She sees Boo as a mockingbird.