The scene of Atticus shooting the mad dog, Tim Johnson, in Chapter 10 has ramifications in other chapters of To Kill a Mockingbird. It initially serves to show Jem and Scout that their father is not just "old" and "feeble," but that he has a special skill that none of their other classmates' fathers have: He was once the best marksman in Maycomb County--a skill about which he has never told his children.
In a fog, Jem and I watched our father take the gun and walk out into the middle of the street...
The rifle cracked. Tim Johnson leaped, flopped over and crumpled on the sidewalk... He didn't know what hit him.
Through Miss Maudie's explanation, the children also discover about humility. When Scout wonders aloud why Atticus wouldn't have told them about his shooting skill, Maudie tells her that
"People in their right minds never take pride in their talents..."
Jem is so proud of his father that he exclaims,
"Atticus is a gentleman, just like me!"
In the following chapter, Atticus reminds Jem that Mrs. Dubose was a true example of courage--"the bravest person I ever knew." He points out the difference between her own style of courage and that of a man with a rifle.
"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."
Much later, as the jury returns to deliver its guilty verdict in the Tom Robinson trial, Scout pictures her father again, and
... it was like watching Atticus walk into the street, raise a rifle to his shoulder and pull the trigger, but watching all the time knowing that the gun was empty.