What does Jem do that shocks Dill and Scout? How does he explain this? How does it establish his maturity?

Jem tells Atticus that Dill is in Scout's room and that he's run away from home. He explains that Dill's mother has a right to know where he is;

Jem was standing in a corner of the room, looking like the traitor he was. “Dill, I had to tell him,” he said. “You can’t run three hundred miles off without your mother knowin‘.”

From this, we come to see that Jem is beginning to understand the repurcussions of actions that aren't thought out.... actions that are thoughtless and impetuous.