Chapter 10 is a very important chapter for Jem and Scout both.  It begins with the description of Atticus. 

"Atticus was feeble:  he was nearly fifty."

"Our father didn't do anything.  He worked in an office, not in a drugstore...he did not farm, work in a garage, or do anything that could possibly arouse the admiration of anyone.

Besides that, he wore glasses.  He was nearly blind in his left eye."

Atticus was an old man who did nothing of importance or excitement to his children.  He couldn't even play football like the other fathers.  However, that all changed when he shot the dog.  Heck Tate wouldn't even take a shot because he wasn't that good with a gun. So when he handed it over to Atticus and made him shoot the dog, Jem's jaw dropped.  He couldn't believe that Heck would ask Atticus (who would never be able to do something that cool) to shoot instead of him.  When Atticus aimed and dropped that rabid dog in its tracks, Jem saw a whole other man in front of him.  His respect grew so quickly, he wasn't able to even speak.  Heck notices this and teases him.

"'What's the matter with you, boy, can't you talk?' said Mr. Tate, grinning at Jem. 'Didn't you know your daddy's--'"

What made him respect Atticus even more was that he never told the kids of his ability.  They didn't know until Heck told them he was the best shot in town.  Atticus was modest, not proud of his talent.  Jem now saw his father as a "gentleman" and aimed to be just like him when he grows up.