We see in chapter six that Jem is beginning to understand more than Scout. Jem is four years older than Scout, so he is more mature than she is. In chapter six, when Jem goes back to get the pants that he had to leave on the fence, he finds them folded over the fence "like they were waiting for him." Jem starts to see that maybe Boo knows more about Jem than he realized.
We really see where Jem understands more than Scout in chapter seven. In this chapter the children start finding the hidden trinkets in the knot-hole in the tree. Jem begins to think that Boo is leaving the gifts for him and Scout. It is the first time that Boo has tried any kind of communication with the kids. When Jem sees Nathan Radley cementing the knot-hole, Jem knows that will be the end of communication with Boo. He stands on his front porch with tears dripping from his face. He cries for the innocent connection he had with Boo and thinks that it is all over now.
To Kill a Mockingbird goes through many themes, but I love the relationship of Boo and Jem and Scout. Jem does much growing up in the book. We see that Jem starts realizing more of the human side of Boo. Unlike Scout, who is still young and fancies the stories, Jem is growing up and understanding a person's feelings more. The covering-up of the knot-hole is the first time Jem shows real emotion. We see from that moment just how much he understands about Boo.