This is a good question. In chapter 10 we read that Scout and Jem saw a dog that was acting oddly. So, they told Calpurnia and she concluded that the dog was mad (probably rabid). Calpurnia, therefore, phoned Atticus to tell him what was going on.
Heck Tate, the sheriff of the town, and Atticus arrived shortly thereafter. It was here that Atticus took a shot and took down the dog. This is also where we learn that Atticus is a good shot and had the nickname of "One shot Finch" when he was younger.
Here is the dialogue:
“He’s gone lopsided,” said Jem.
Calpurnia stared, then grabbed us by the shoulders and ran us home. She shut the wood door behind us, went to the telephone and shouted, “Gimme Mr. Finch’s office!"
“Mr. Finch!” she shouted. “This is Cal. I swear to God there’s a mad dog down the street a piece—he’s comin‘ this way, yes sir, he’s—Mr. Finch, I declare he is —old Tim Johnson, yes sir... yessir... yes—”
The symbolic meaning of this text, which we will see later, is that Atticus is one of the few people in town who will protect people from madness. The madness in view is racism and injustice. Miss Maudie makes this point eloquently:
“I simply want to tell you that there are some men in this world who were born to do our unpleasant jobs for us. Your father’s one of them.”