Shortly after the Tom Robinson trial, Bob Ewell confronted Atticus outside the post office, where he cursed him, spat in his face, threatened to fight him and promised to kill him. Atticus turned the other cheek and walked away, but Jem and Scout were worried about the death threat. Scout suggested that since Atticus was once the deadest shot in the county, he should get a gun for protection. Jem assured her that Atticus wouldn't carry one because "he told me havin' a gun around is an invitation to somebody to shoot you." But Jem decided to suggest that Atticus borrow one anyway. Atticus' response: "Nonsense."
After Tom Robinson is unjustly found guilty of the rape of Mayella Ewell, Mr. Bob Ewell (the young woman's father and the drunkard who actually beat her) stops Atticus (who defended Tom at his trial) in the street outside the post office, spat in his face, and promised him that "he'd get him if it took the rest of his life." Atticus responded peacefully to this attack, merely wiping his face with a handkerchief, allowing Ewell to finish his rant, and then carrying on with his day.
Scout knows that her father "was the deadest shot in the country one time," but that he doesn't believe in carrying a gun, considering it to be an invitation for someone else to shoot you. Scout and Jem ask Atticus to borrow a gun, but Atticus simply responds, "Nonsense." They then try various other methods: Scout throws a fit and cries, and the two mope around the town.
This finally makes Atticus realize that his children are genuinely concerned for his welfare, although Atticus quickly puts this, too, to rest, stating that he'd rather be the target of Ewell's anger than have Ewell's children suffer for it and claiming that, "Nobody has much chance to be furtive in Maycomb."
Atticus is wise enough not to be scared off by Ewell's words and realizes that they are just that: the empty threats of a mean drunk and a terrible liar.