Chapter ten can be interpreted as an "awakening". When Atticus kills the dog, both Jem and Scout are proud of their father. Prior to that event the children are busy comparing their father to other fathers. Neither of them realize just how significant their father is. The dog killing incident allowed the children to feel their father's courage. It is that incident which will ultimately allow the children to understand the absolute courage it must have taken their father to represent Tom Robinson. It is in this chapter the children are able to comprend thier fathers' warning or perhaps advise, never kill a mockingbird. Atticus explains to the children that mockingbirds only provide the joy of sound for us, they have no ill will. Atticus proposes a very simple concept to his children, in which they will transform its child like simplicity into its true and human meaning.
Off the bat, we see that Jem and Scout are introduced to the new side of their father, Atticus, that they had never been exposed to before.
The irony that was displayed when Atticus shot the dog was great, in that, Atticus constantly mentioned, (something along the lines of) "Don't judge a person until you walk a mile in their shoes."
Following this scene, Maudie tells the kids about Atticus' nickname, "One-shot-finch," and Jem demands that Scout NOT brag or tell anyone about it.
This idea further implies the characterization of Jem... He's becoming a more responsible adult and is starting to realize how the real world works. He understands that bragging isn't going to get them anywhere, except confusion (or putting Atticus in a spot where he'd have to explain why he didn't tell his own kids about how good with a rifle he was)