There are several examples to choose from. One example comes from chapter 11 when Atticus makes Jem read to Mrs. Dubose as punishment for destroying her camelia bushes after she insulted Atticus. This example of courage is important because it sets up what courage really is for the rest of the novel.
In a fit of anger, Jem destroys Mrs. Dubose's camelia bushes after she insults Atticus. As his punishment, he is to read every afternoon to her six days a week for a month. Jem is horrified that he has to sit and read while Mrs. Dubose drools and says terrible things to him about his father. At first Jem is relieved when Mrs. Dubose falls asleep before his two hours are up and he is allowed to leave. However, as time progresses, Mrs. Dubose stays conscious longer and longer and eventually extends Jem punishment for another week. Finally, Mrs. Dubose dismisses Jem.
One evening as Atticus is reading to Jem and Scout, he is called to go to Mrs. Dubose. He returns with news that Mrs. Dubose has died. She sends a box for Jem with a camelia in it. He responds by calling her a "hell-devil" and wonders why she can't leave him alone even after her death. Atticus then explains to Jem that
I told you that if you hadn't lost your head I'd have made you go read to her...I wanted you to see what real courage is, instead of gettng the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do.
This lesson of courage is important because it serves a double purpose. Atticus is preparing Jem and Scout for the battle that he and they will face when he defends Tom Robinson. Atticus knows it is a battle he can't win, and he wants the kids to know that it is a battle worth fighting for. Also, the hurtful things Mrs. Dubose says to Jem prepares him for the comments the rest of the town will say. This teaches Jem to hold his temper and not take the comments personally.