In the first sentence, Scout says that Jem had his arm broken when he was 13. She doesn't really mention the rest of it until the end of the book, and the encounter between the Finch children and Bob Ewell. Once the novel concludes, we understand that Jem broke his arm in the scuffle with Ewell, as he tried to protect Scout from Ewell and escape Ewell's attack.
Harper Lee has a future, adult Scout narrate To Kill a Mockingbird. In the beginning of the book, she talks about Jem's broken arm, which leads into an exposition of the Finches' ancestry and how they ended up in Maycomb County. It's as if she gets side-tracked and forgets about explaining the way Jem broke his arm until the end. As a result, this teases the reader into wondering what happened, but the answer isn't given until the very end of the story. A reader could forget about it by the time he or she finishes the book. If it is remembered, it is like finding a golden nugget. It's good storytelling structure for sure.
She doesn't revisit the effects of the broken elbow at the end of the book, either. Readers have to go back to the beginning to remember the following:
"When he was nearly thirteen, my brother Jem got his arm badly broken at the elbow. When it healed, and Jem's fears of never being able to play football were assuaged, he was seldom self-conscious about his injury. His left arm was somewhat shorter than his right; when he stood or walked, the back of his hand was at right angles to his body, his thumb parallel to his thigh" (3).
It is interesting to note that Jem breaks the same arm as Tom's crippled arm, but Jem has some ability still left in his arm after his accident, and Tom never did. Nevertheless, Jem and Scout looked back on these years together and Scout said that the Ewells started it all, but Jem says the problems in Maycomb started long before the Ewells even existed.
At the end of the novel, though, the detailed events show that Bob Ewell tried to take revenge on Atticus Finch's children by attacking them with a kitchen knife. Unfortunately for him, the Finch children had a friend nearby who seemed to be looking out for them and saved them from a murderer that night. Jem was lucky to be living with a broken arm, because he could have died that night.
The first sentence mentions Jem's broken arm, and that arm was broken because of the events that unfolded and how they got away from Bob Ewell. Bob Ewell was the cause of the shift of the town and the children as a whole and throughout the story she recounts the experiences and what mark it left on her.