Give a specific example of an instance in To Kill a Mockingbird that shows what kind of boy Jem is and explain its importance.
In Chapter 10, Jem understands why Atticus has never bragged about his marksmanship skills to his children. It's because
"Atticus is a gentleman, just like me!"
Perhaps there is no better illustration of Jem's growth into gentlemanly maturity than in Chapter 28, when he escorts Scout to and from the Halloween pageant. Atticus was too tired to walk the children himself, something he would have normally done during the evening hours. So, Jem stepped in for his father, walking Scout past the spooky Radley house in the darkness. When they heard the footsteps on their way back and were then attacked by the stranger, Jem did his best to protect his sister. After the attacker first assaulted Scout, she called for help, and Jem came to her rescue.
... I felt Jem. He was up like lightning and pulling me with him but... we didn't get very far.
Jem suffered a broken elbow but earned Scout's everlasting gratitude. He was a brave big brother of which any younger sister would be proud.