Answer:
Atticus's advice to "climb into someone's skin and walk around in it" means that compassion is based on sympathy, on being able to put yourself in the other person's place and understand why they act the way they do even if you don't agree with it.
In Chapter 3 of To Kill a Mockingbird, Atticus provides fatherly wisdom. In this case, he's trying to tell Scout that Miss Caroline (her teacher) was probably just trying to do her best in a new place, whose ways she doesn't yet understand.