What events mature scout, dill, & jem? (tkam)

There are multiple occasions in To Kill a Mockingbird that influence Scout, Dill and Jem's maturity. The most important would be:

Tom Robinson's trial and death.

The three children become aware of the racial intolerance present in their society, in all its cruelty. Tom Robinson is accused of physically assaulting Mayella Even, and found guilty, despite the insufficient evidence to prove his guilt.

The story around Boo Radley.

Boo Radley, a mysterious neighbor who never leaves his house and strikes fear into the children, turns out to be the one who rescues Jem and Scout when Bob Ewell attacks them. The children learn not to believe everything they are told.

The death of Mrs. Dubose.

Mrs. Dubose is a hostile neighbor that insults Jem and Scout. Angry at her, Jem cuts off her camellia bushes. When his father finds out, Jem is forced to apologize and to read to her every day after school. Mrs. Dubose is ill, and eventually dies. Her death reminds the children that this woman had a difficult life, and, by refusing to take morphine, tried to die with a shred of dignity.