The theme of chapter six is one of growth and development, particularly for Jem. The last night that Dill is in town signals an eventful evening. He and Scout and Jem decide to go over to the Radley house to see if they can see anything and when Nathan Radley chases them away with gunshots, Jem loses his pants on the fence.
In the process, he has to then lie to Atticus but he chooses this over telling the truth because he feels it is more likely to protect the trust Atticus has in him and he now knows how much he values that trust and respect. He also has to return to the Radley place, facing his fears, in order to get the pants and keep Atticus from finding out what really happened.
As Jem faces these fears and makes these priorities, he demonstrates his growth from boy to man, a change that Scout notices when she notes that that evening was the time that she and Jem began to grow apart.