Jem and Scout grow up in a variety of ways during this novel. The first one takes place when Nathan Radley cements the knothole, preventing Boo from leaving anymore gifts for the children. Scout notices that Jem is crying on the porch, and leaves him alone to do so. While Scout may not understand the full impact of this situation, Jem understands that Boo was just trying to reach out to someone, and his brother, who is his keeper, is trying to prevent even the most innocent and benign communication with the outside world.
Jem receives another big shock at the end of the trial--the verdict breaks his heart. He, Scout and Dill feel sickened by their town after the jury finds Tom Robinson guilty. They see the neighbors gossiping, and in addition to the obviously incorrect verdict, the town is gossiping about the trial, Atticus and anything to do with it. Jem and Scout felt like the lived in the safest place with the best people in the world--Jem says he felt like he was a caterpillar wrapped up in a cocoon--but they now feel sickened by the behavior of their neighbors.
The last revelation revolves around Boo Radley. Jem and Scout used to believe that he was a scary, creepy neighbor that would harm them if they got too close to his house. However, after the night the children were attacked by Bob Ewell, the children realize that Boo is a kind neighbor, and Scout, by standing on the Radley porch, comes to take Atticus' advice about seeing things through another person's eyes. She sees the neighbor how Boo would see it, and she's not scared of him anymore.