One of the most significant themes in To Kill a Mockingbird is courage, and Harper Lee uses many of the characters and circumstances in her novel to demonstrate all facets of courage.
There is a physical courage which is demonstrated by Atticus standing in the middle of the street, facing off with a rabid dog armed only with a shotgun. This is an especially impressive feat to his children, of course, but Atticus now has to work extra hard to show them that there are other, more important kinds of courage.
The incident Jem has with Mrs. Henry Lafayette Dubose demonstrates another kind of courage. Here is an old woman who, we discover, is addicted to morphine. She is cantankerous, rude, and prejudiced; however, she also has a kind of inner strength which enables her to kick a long-time addiction in order to die free. Atticus tells Jem:
I wanted you to see what real courage is, instead of getting 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 is timely advice because of the upcoming trial.
Atticus, of course, demonstrates all kinds of courage. Miss Maudie tells Scout that the town is cowardly because it lets Atticus do the "dirty work" of standing up for what is right when they either do not want to or are unwilling to become a target for their neighbors, friends, or customers.
Atticus does not just go through the motions of representing Tom Robinson at his trial; instead he does what he knows is right: he defends an innocent man. This puts his own life at risk, as well as the lives of his children. He is confronted with a mob at the courthouse, he is spit upon by Bob Ewell, and he risks losing the respect of everyone in town that disagrees with him--including his own sister and her family. Yet he continues.
Miss Maudie shows courage when she refuses to be pressured by the "foot-washin' Baptists" who try to shame her out of growing her flowers. When they shout Bible verses at her, she responds with other Bible verses. She is not intimidated by these bullying tactics, and she courageously confronts them in her own backyard, so to speak.
Boo Radley demonstrates extraordinary courage when he saves the Finch children from being killed by Bob Ewell. Even more, he kills Ewell in the process. There is no doubt that this is a courageous and selfless act.
Even Walter Cunningham's dad demonstrated a rather extraordinary courage in this novel. Although he was kind of the ringleader of the group that came to cause trouble for Tom Robinson at the jail, Atticus placed him on the jury of Tom's trial. The expectation is that this jury will come back with an inevitable guilty verdict; after all, a white woman accused a black man of raping her, so the black man must be guilty.
Instead, Walter Cunningham is the juror who prolongs the verdict long enough to give Atticus some hope. Though Cunningham was unsuccessful in changing his fellow jurors' mind, he was able to hold them off for a time, obviously because he believed Tom was innocent. This simple act gives us all hope that one day things would be more equitable for blacks.
Scout, Jem, and Dill display some moments of courage in their antics with the Radley house, but often those are more bravado-driven than prompted by true courage.
If you need more thoughtful insights and analysis of this classic novel, check out the excellent eNotes sites linked below.