Both Jem and Scout mature greatly throughout To Kill a Mockingbird, though Jem arguably makes larger leaps in the process. One of the greatest influences on the maturation of Jem and Scout is their father, Atticus. Not only does Atticus talk to his children as if they were adults, but also he encourages them to think beyond themselves. He tells Jem and Scout to put themselves in other people's shoes, to see the situation from the other person's perspective, before making a conclusion. This teaching is one of the catalyst for maturity in the children.
The situation itself also contributes to Jem and Scout maturing greatly throughout the novel. They are put into an intense situation, and have to deal with prejudice, name-callings, bitterness, violence, etc. Whenever children are exposed to adult situations, the rate of natural maturity increases.
Other characters also add to their development, mostly by reinforcing the teachings of Atticus. Miss Maudie and their aunt both contribute to the children's growth throughout the novel, as does their growing and changing relationship with Book Radley.