I tried to climb into Jem’s skin and walk round in it

This sentence is about Scout trying to see life through Jem’s eyes. Scout wants to understand what Jem is feeling and thinking and essentially, what it’s like to be Jem. This also relates to a comment which Scout remembers Atticus saying in Chapter Thirty One; you never really know a man until you stand in his shoes and walk around in them.  Scout remembers this after she’s just walked Boo home and while she is standing on the Radley porch, she feels she finally understands all the components of the mysterious Arthur Radley at this moment.