The first sentence of the book states,
"When he was nearly thirteen, my brother Jem got his arm badly broken at the elbow."
It is in the last chapters of the book that Jem breaks his arm, so that is how that sentence ties in to the end of the book. Hopefully, if you have read the final chapters, you will understand the chain of events that led up to Jem getting his arm broken; in general, Bob Ewell attacks Jem and Scout, and in the scuffle, Jem gets his arm broken. Specifically, the actual event of Jem breaking his arm occurs in chapter 28 of the book; more details about the event come out in chapters 29 and 30. You can't read "To Kill a Mockingbird" without reading those chapters. They bring everything that the entire book has talked about all together in a very dramatic climax. In light of that, I would hate to just outright state what happened. Instead, I encourage you to quickly read through those chapters on your own if you haven't already, and I also provided a link below to an analysis of those chapters that will help to explain-clearly and concisely-just exactly what happens. Good luck!