Over the course of the novel, Jem's biggest change comes from his transition from a young boy into a young man. When we first meet Jem he is ten.... by the end of the novel, he is thirteen. From the start, Jem and Scout are best friends. When Dill arrives in Maycomb, all three hang out and play together. As the novel progresses, Jem starts to brush his sister off, noting that she's a girl, and sometimes even encouraging her to act like one.
After the trial begins, Jem grows up even more. He begins to understand injustice, disappointment, and ill intent. Jem learns that right doesn't always win, and that good people sometimes do bad things. He acquires a deep respect for his father, a respect far beyond Atticus as a father..... he respects him as a man.