This is a good question. There is growth and maturity that takes place in Jem. He is a different person at the end of the story.
In the beginning of the novel, Jem is a young boy who likes to play sports and have fun. However, he is a natural leader. Scout and Dill follow him. Also he is daring. Scout says of him that he never turned down a dare. So, when Dill dared him to touch the Radley's front door, Jem did it.
As the novel progresses Jem matures, especially during the trial scene. When Tom Robinson loses, Jem takes it hard. Here is a quote that shows an interaction between Jem and Atticus. Jem is maturing and his character is forming. He is becoming a man of convictions.
“Doesn’t make it right,” said Jem stolidly. He beat his fist softly on his knee. “You just can’t convict a man on evidence like that—you can’t.”
“You couldn’t, but they could and did. The older you grow the more of it you’ll see. The one place where a man ought to get a square deal is in a courtroom, be he any color of the rainbow, but people have a way of carrying their resentments right into a jury box. As you grow older, you’ll see white men cheat black men every day of your life, but let me tell you something and don’t you forget it— whenever a white man does that to a black man, no matter who he is, how rich he is, or how fine a family he comes from, that white man is trash.”
Finally, at the end of the book, Jem seeks with all his might to protect his sister from Bob Ewell. In the process, his arm is broken. This shows that Jem is now a protector.