One thing that motivates Jem is his pride. He wants to be seen as more adult-like. He wants to be trusted. An example of this is when he leaves his pants on Boo Radley’s porch accidentally. That day, he decides to go back to get them. Scout is worried about him getting killed, and tells him he is better off being punished. Jem explains why that’s no good.
He blew out his breath patiently. "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)
Jem is actually not concerned with getting spanked. He just does not want Atticus to be disappointed in him. He is actually acting maturely in a way. He is being brave, because he wants to be seen as more adult-like and responsible. He does not want to let Atticus down, which is a mature attitude.
Jem shows bravery in going to the fence at night. The opinion of his father is more important than anything which might happen to him there. He is beginning to prioritize values in his life. (enotes ch 6)
Jem is growing up, but also growing apart from Scout. Scout begins to understand him less and less at this point. She is not at his level yet.
We see this maturity throughout the rest of the book, as Jem begins to act more adultlike and stands up for his father and protects his sister.