Miss Maudie tells Scout that Atticus is “the best checker-player in this town” and when they were growing up he “could beat everybody on both sides of the river” (ch 10). Scout is surprised to hear this, because she and Jem regularly beat Scout at checkers. Miss Maudie tells her it is time she learned that Atticus let them beat him.
The significance of this section is that the children do not know as much about their father as they think they do. They consider him old and feeble. They don’t realize he’s a crack shot with a rifle, an excellent checker player, and a musician. Part of growing up is realizing who your parents really are, and in Scout’s case realizing how important her father is to the town.
Atticus's checker-playing skills are mentioned several times during To Kill a Mockingbird. In Chapter 10, Jem and Scout are concerned because their father is "feeble" and doesn't seem to have any real interests or talents aside from his lawyering skills. When Scout asks Miss Maudie what else he can do, she tells Scout that Atticus is an expert at making an airtight will; that he can play the Jew's harp; and that he's "the best checker player in this town." This is news to Scout. "Good Lord, Miss Maudie, Jem and me beat him all the time." But Maudie tells her that
"It's about time you found out it's because he lets you [win]." (Chapter 10)
Scout is reminded of Atticus's checker playing later when he asks the crowd of men gathered in his front yard "Do you really think so?"
This was Atticus's dangerous question. "Do you really think you want to move there, Scout?" Bam, bam, bam, and the checkerboard was slept clear of my men. (Chapter 15)
And the next day, she hears the same question again when Atticus directs it to lynch mob.
"Do you really think so?"
This was the second time I had heard Atticus ask that question in two days, and it meant somebody's man would get jumped. (Chapter 15)