In Harper Lee's To Kill a Mockingbird, one event that changes Jem is the realization that Arthur (Boo) Radley is reaching out to the children in his own special way.
The first time Jem realizes Arthur is reaching out to the children is the night he and Dill decide to sneak onto the Radley property to try and get a glimpse of Arthur through the window, bringing an unwilling Scout along with them. When shots ring out, the three children flee in terror. During flight, Jem gets his pants caught on the barbed wire fence and must abandon them to escape. At two o'clock in the morning, Jem decides to go back to the Radley property to try to retrieve them. Later, he explains to Scout the surprising condition he found his pants in, which he left "all in a tangle":
When I went back, they were folded across the fence ... They'd been sewed up. Not like a lady sewed 'em, like somethin' I'd try to do. (Ch. 7)
These clues signify that Arthur had sewed up Jem's pants for him in an act of kindness.
During Scout's second grade year, Jem also begins to realize the items he and Scout are finding in the knothole of the oak tree on the Radley lot are actually gifts Arthur is intentionally leaving for the children. The biggest clue is when the children find bars of soap in the knothole that had been carved to look just like the children. Jem knows perfectly well that Arthur is the only one in the neighborhood reputed to have such excellent whittling skills.
As soon as Jem brings himself to realize that Arthur is silently reaching out to the children through gifts and kindness, he decides to leave Arthur a thank-you note in the knothole and is absolutely devastated to find that Arthur's older brother Nathan had filled in the hole with cement. Jem is so devastated he has no way to thank Arthur that it moves him to tears, as Scout notes at the end of Chapter 7.
But, Jem's tears are a sign that he is growing up and has been changed by the experience. His tears signify he feels guilty for having mocked Arthur through the game he and Dill invented and has come to see beyond the rumors and myths surrounding Arthur: Jem has come to see Arthur as a kind and caring person, albeit mysteriously reclusive for reasons of his own.