In chapter 30, after Scout has recounted the events under the tree (the fight with Mr. Ewell which ended in his death) Mr. Tate finalizes the events with:
"Bob Ewell fell on his knife. He killed himself."
Atticus will not take this answer though, because he (at first) thinks it is Jem who killed Mr. Ewell. After much argument, Mr. Tate indirectly infers that it was actually Boo who stabbed Mr. Ewell, therefore he will maintain that it was an accidental suicide. When Atticus asks Scout if she can "possibly understand," she responds with:
"Yes sir I understand... Mr. Tate was right... it'd be sort of like shootin' a mockingbird, wouldn't it?"
This pattern of events and final quote of Scout's shows she finally has an understanding of who Boo is, and how the small town of Maycomb works.
There are several good examples of Scout's ascendancy toward adulthood in To Kill a Mockingbird. Perhaps the best one comes in the final chapter, when she stands on the Radley porch looking out over her neighborhood.
I had never seen our neighborhood from this angle... As I made my way home, I felt very old... As I made my way home, I though Jem and I would get grown but there wasn't much else left for us to learn, except possibly algebra.
Another example comes during the Missionary Circle meeting after Atticus has announced the death of Tom Robinson (Chapter 24).
I carefully picked up the tray and watched myself walk toward Mrs. Merriweather. With my best company manners, I asked her if she would have some.
After all, if Aunty could be a lady at a time like this, so could I.