Jem ages from 10 to 13 over the course of To Kill a Mockingbird, a period of great change in any child's life. Jem is no exception to this rule. Interestingly, the changes he undergoes are seen from the point-of-view of a younger sister, which gives a unique perspective on his growth.
Jem represents the idea of bravery in the novel, and the way that his definition changes over the course of the story is important. The shift that occurs probably has as much to do with age as experience, although the experiences provide a better framework for the reader. When the story begins, Jem's idea of bravery is simply touching the side of the Radley house and then only because "In all his life, Jem had never declined a dare." But as the story progresses, Jem learns about bravery from Atticus facing a mad dog, from Mrs. Dubose's fight with addiction, and from Scout's confrontation with the mob at the jail, among others. And along the way, he grows from a boy who drags his sister along as a co-conspirator to a young gentleman who protects his Scout and tries to help her understand the implications of the events around her.
His own sister finds Jem a genuinely likeable boy, if sometimes capable of "maddening superiority." He very much wants to be like his father, and plans to follow him into law. He idolizes Atticus and would rather risk personal injury than disappoint his father. As he grows older, he begins to do what is right even though his decision may not be popular. For instance, when Dill sneaks into Scout's bedroom after running away from home, Jem can only say, "'You oughta let your mother know where you are'" and makes the difficult decision to involve Atticus. Afterward, he's temporarily exiled by his friends, but he maintains the rightness of his decision without apology.
Like many adolescents, Jem is idealistic. Even after Atticus' long explanation about the intricacies of the Tom Robinson case, Jem is unable to accept the jury's conviction. In fact, he is ready to overhaul the justice system and abolish juries altogether. Wisely, Atticus doesn't try to squelch or minimize Jem's feelings; by respecting his son, Atticus allows Jem to better cope with the tragedy. Still, Jem turns on Scout when she tells him about Miss Gates' racist remarks at the courthouse, shouting, "'I never wanta hear about that courthouse again, ever, ever, you hear me?'" His coping skills are still developing, and his family is the one group that gives him the room that he needs to hone them.
Ironically, Jem, who so strongly identifies with Tom Robinson, is the only person in the story who is left with physical evidence of the whole event. More ironic still is the fact that Jem's injury leaves "His left arm . . . somewhat shorter than the right" just like Tom Robinson's, and Tom Robinson sustained his injury at approximately the same age. That the man responsible for breaking Jem's arm was also responsible for sending Tom to prison (and indirectly, responsible for his death) serves to drive the irony home.
The adult Jean Louise doesn't provide much insight into the adult Jeremy Atticus Finch, but from the fact that the story begins with their disagreement over when various events started, the reader can assume that they maintained a similar relationship into adulthood.