In Harper Lee's To Kill a Mockingbird, Jem and Scout's relationship changes.
First, Jem is going through puberty. (He shares the news of hair growing on his chest with Scout.)
The story primarily revolves around the court case of Tom Robinson, a black man accused of a crime he did not commit. The story takes place in the South, not too long after the end of the Civil War, and during the Great Depression. Poverty is prevalent, memories are fed with hate on a regular basis, and Atticus Finch is chosen to represent Tom.
Scout and Jem are accustomed to seeing their father in court, and they have a good understanding of how to read witnesses as well as their father. However, Atticus has spent almost his entire career avoiding criminal cases.
Scout is younger than Jem, and as the travesty of the court trial continues, and Tom is tragically found guilty of an imaginary crime, Jem is forced to face the realities of the adult legal system and the hatred in men's hearts. Scout is affected to a certain extent, by tends to lean more to sleeping in the courtroom, while Jem becomes more and more invested in the outcome. It is here that evil personified is introduced to the children, though at the time they are unaware of its presence.
Jem, because of his age, is better able to appreciate the lesson to be learned in Mrs. Dubose's sickroom after he destroys her flower bed. He is forced, in essence, to look into the face of physical addiction and the strength of the human soul in fighting that demon, and winning, something Scout doesn't appreciate on the same level as Jem.
Finally, when the evil in the form of Mr. Ewell steps out of the courtroom and into the night, pursuing the children with the intent to kill them, in a split second Jem is galvanized into the world of adulthood as he is called upon to defend not only his own life, but that of his sister, as Bob Ewell tries to stab them.
While reading carefully, there are many subtle hints of the changes that separate the children as they grow over the course of the story; there are other much more significant events that show Jem's coming of age. At the same time, it is Scout's ability to maintain some of her innocence and honesty (while Jem and she grow apart) that so enthrallingly bring the characters and plot to life.