The punishment is reading to Mrs. Dubose for two hours a day.
When introducing her neighbors, Scout describes Mrs. Dubose as “plain hell” (Ch. 1). This tells us that she is not a friendly person, but we do not get the full picture of what it means until she begins spewing her vitriolic insults at Jem and Scout later. She lives two doors up the street and Scout considers her “the meanest old woman who ever lived” (Ch. 4).
Jem and I hated her. If she was on the porch when we passed, we would be raked by her wrathful gaze, subjected to ruthless interrogation regarding our behavior, and given a melancholy prediction on what we would amount to when we grew up, which was always nothing. (Ch. 11)
The problem occurs as the Tom Robinson trial approaches when Mrs. Dubose provides Scout and Jem unsolicited opinions about their father’s defending a black man, which are of course laced with racism. Jem loses it and attacks her flowers with Scout’s baton. He is tired of hearing people insult his father for defending a black man in the trial.
Atticus made Jem go “have a talk with Mrs. Dubose,” which Scout considered a terrible punishment. She was certain Jem was going to be “murdered with a Confederate Army relic.” Jem went. When he returned, he told Atticus that he had cleaned it up, but Mrs. Dubose had asked him for something.
“Atticus,” he said, “she wants me to read to her.”
“Read to her?”
“Yes sir. She wants me to come every afternoon after school and Saturdays and read to her out loud for two hours. Atticus, do I have to?”
“But she wants me to do it for a month.” (Ch. 11)
Later, the children learn that Mrs. Dubose was trying to kick a morphine habit and that the reason she wanted Jem to read to her was to provide her a distraction. Atticus considered her a good role model of courage, despite that fact that she disagreed with him and he disagreed with her on the subject of the trial. She stood up to her addiction and won her fight, and he admired that.