My favorite description of Jem depicts both a strong physical characterization as well as one which reveals a personality not unlike his father's. It can be found in Chapter 15 on the night in which the lynch mob arrives to take Tom from the jail. Atticus orders Jem to take Scout and Dill and go home, but his son's stubborn nature wins out. Jem refuses.
As Atticus's fists went to his hips, so did Jem's, and as they faced each other, I could see little resemblance between them: Jem's soft brown hair and eyes, his oval face and snug-fitting ears were our mother's, contrasting oddly with Atticus's graying black hair and square-cut features, but they were somehow alike. Mutual defiance made them alike. (Chapter 15)
Another telling description of Jem's personality is found in the opening paragraphs of Part Two (Chapter 12). Jem and Scout are beginning to "part company," and Scout wonders if it is a tapeworm that is causing his unusual behavior. Both Atticus and Calpurnia explain to Scout that "Mister" Jem is simply "growin' up"--he is approaching puberty--and that he needs to spend time alone away from his sister.
He was difficult to live with, inconsistent, moody. His appetite was appalling, and he told me so many times to stop pestering him, I consulted Atticus...
Overnight, it seemed, Jem had acquired an alien set of values and was trying to impose them on me. (Chapter 12)
Well Jem is very kind but has a rebellious side to him. We see this later in the book. He seems like he try's to act older then he really is which could mean that he is in adolescence.
Hope this helps!!! =)