What did Scout and Jem learn about Atticus in Chapter 10 of Harper Lee's To Kill a Mockingbird, and how did they learn this about him?

In Chapter 10 of Harper Lee's To Kill a Mockingbird, Atticus astounds both his children through demonstrating he has excellent marksmanship by shooting a rabid dog in one shot, thereby protecting his children and his whole neighborhood. Prior to this moment, both his children had believed Atticus was nothing more than a "feeble" old man, incapable of accomplishing anything of significance. Due to their age differences, Jem and Scout learn different things from the experience. Scout, being younger, only learns that her father is more capable than she believed him to be. Jem, being older, learns lessons in courage and gentlemanly behavior.

After witnessing her father's shooting skills, Scout is puzzled as to why Atticus kept his skills a secret and doesn't shoot any more. She tries to alleviate her confusion by having a conversation about it with Miss Maudie. In answer to Scout's question as to why Atticus never hunts anymore, Miss Maudie explains that Atticus realizes his gift of marksmanship places him at an "unfair advantage over most living things." Miss Maudie further explains that, since Atticus values life, he decided not to shoot until he absolutely "had to." After hearing that, Scout can understand why Atticus doesn't shoot anymore, but she can't understand why he has kept his abilities a secret all these years and next says, "Looks like he'd be proud of it." But Scout is too young to understand that, due to Atticus's humility, Atticus is unable to be proud of a God-given talent that allows him to kill at will. Hence, all Scout learns from the experience is that Atticus is able to do things she never knew about before.

In contrast, Jem, being older, is able to understand exactly why his father objects to using his sharpshooting skills. Jem explains to his sister that Atticus is not proud of his skills because, as he says to Scout, "Atticus is a gentleman, just like me!" (Ch. 10). In saying this, Jem means that Atticus is acting gentlemanly in refusing to kill living things, since to be gentlemanly is to be caring and considerate. Therefore, through learning more about his father, Jem also develops a greater understanding of what it means to be a gentleman.