The story actually begins with a description of Jem’s injury when he was fourteen, and his reaction to the events of the book as an adult. Then Scout describes a time a few years back.
At first, Jem spends a lot of time with Scout. He is more mature, but still childish and playful. He plays make-believe games acting things out with Scout and Dill, both of whom are younger. Jem has a good imagination.
Jem gave a reasonable description of Boo: Boo was about six-and-a-half feet tall, judging from his tracks; he dined on raw squirrels and any cats he could catch, that's why his hands were bloodstained … (ch 1)
Jem does mature as Scout gets older, and comes to take on a more parental role. He often accuses Scout of acting like a girl. Scout looks up to him, and confides in him.
Having never questioned Jem's pronouncements, I saw no reason to begin now. (ch 2)
Jem is brave. When he loses his pants, he risks getting killed (since the children think Nathan Radley will shoot them), to go get them so that Atticus will not find out that he disobeyed him about going to the Radleys. Jem is not concerned with being punished, he just does not want to let Atticus down.
"I- it's like this, Scout," he muttered. "Atticus ain't ever whipped me since I can remember. I wanta keep it that way." (ch 6)
This is an example of how Jem matures and distances himself from Scout. Yet he still has moments of childish rage and destruction, such as when he destroys Mrs. Dubose’s flowers after she insults them.
During the trial, Jem is highly interested. He wants to be a lawyer, and he has a strong sense of justice. He follows the trial closely, and assumes that since Atticus makes a good case, Tom Robinson will be acquitted. When he is convicted, Atticus is annoyed.
It was Jem's turn to cry. His face was streaked with angry tears as we made our way through the cheerful crowd. "It ain't right," he muttered… (ch 22)
Jem has to come to terms with the reality of racism. It is when he really grows up.