In chapter eleven of To Kill a Mockingbird by Harper Lee, Jem and Scout have an encounter with an old woman who will change Jem's perspective on life. Atticus has agreed to defend Tom Robinson, and opinions in town about that decision are mixed. It is actually a compliment to Atticus that people are upset, because it means they know his character and therefore know he intends to truly defend a Negro rather than just go through the motions as so often happens in these types of cases.
Mrs. Henry Lafayette Dubose is a cantankerous old woman who sits on her porch and makes a sport out of insulting Jem and Scout every time they walk by her house. She says terrible things about them and their father, Atticus, insulting their heredity and personal hygiene, as well as their father's choice to defend Robinson. For example, she says:
“Yes indeed, what has this world come to when a Finch goes against his raising? I’ll tell you!” She put her hand to her mouth. When she drew it away, it trailed a long silver thread of saliva. “Your father’s no better than the niggers and trash he works for!”
Horrible as this is, it is a day when she says nothing--is not even on the porch-- when Jem erupts. He has been learning how to be a gentleman and practicing that skill quite diligently, but being insulted by an adult is just too much for him to take, and Scout thinks the only "explanation for what he did was that for a few minutes he simply went mad."
He and Scout had just been downtown, and Scout has a baton she is twirling on the way home. When they pass Mrs. Dubose's house, Jem grabs the batons and thrashes the woman's camellias "until the ground [is] littered with green buds and leaves." Scout is screaming and he screams back at her and finally kicks her in his anger. He snaps the baton in half and storms home. It is an outrageous display of anger, something which Atticus later says he expected from Scout rather than Jem.
Of course Mrs. Dubose knows who committed this act, and she is quick to let Atticus know what happened. Jem's punishment is to go read to Mrs. Dubose for two hours after school every day and on Saturday.
Though Jem does not want to do it, he does, and Scout goes with him. It is an unpleasant experience, but it gets a bit better over time. What they discover later is that Mrs. Dubose was addicted to morphine (for pain) and was courageous enough to want to die without being addicted to anything. Atticus wants his children to see that true courage is not just wielding a gun or performing some great feat of valor. Mrs. Dubose demonstrates courage by defeating her body's cry for the drug to which she is addicted.