Dill, Jem, and Scout stand outside the Radley house thinking of ways they can get Boo Radley to come out. This is important because it is the start of their large curiosity for Boo Radley (17).
At School, Miss.Caroline tells Scout that she can't read with Atticus anymore because he isn't a teacher. This is important because this event causes Scout to dislike school now (22).
Scout tells Atticus at home the next day that she dosn't think she needs to go to school anymore. This is important to her character because this feeling stems from her love for reading (34).
Jem and Scout find a purple velvet box in the tree filed with pennies. This is important because it is the beginning of Jem and Scout's relationship with Boo Radley (39).
Atticus calls Jem and Scout into the house and tell them that it isn't right to make fun of Boo Radley to the whole town. This is important because it shows that Atticus feels sympathy towards Boo and wants to teach his kids to feel the same (54).
Jem and Scout are holding up Dill so that he can look into the Radley's window. This is important because Jem and Scout are going against Atticus's rules about leaving the Radley's alone (57).