The title of the novel comes from Chapter 10, and it is Atticus who first uses the phrase "to kill a mockingbird." It comes in a lesson to Jem about using his new gun.
Shoot all the blue jays you want, if you can hit 'em, but remember, it is a sin to kill a mockingbird (90).
Later, Scout asks Miss Maudie what Atticus means by this "sin." Miss Maudie explains that mockingbirds are completely innocent songbirds. They don't do anything to harm anyone, therefore, they do not deserve to be shot at for sport.
Later, in Chapter 30, after the attack scene involving Scout, Jem, and Mr. Ewell behind the school, Sheriff Tate insists that Mr. Ewell died by falling on his knife.
Atticus knows this is not the truth. He also knows that Scout knows this. When he asks her if she can possibly understand she responds with:
Well, it'd be sort of like shootin' a mockingbird wouldn't it? (276).
In this moment, Scout shows that she understands that Boo Radley is as innocent as a mockingbird. He's never done anything to harm anyone, and he doesn't now deserve to be made a target for anything.