I saved Scout and Jem from someone beating them up in the woods.
Trying to show everyone that he isn't a bad person. Everyone thinks that he is because there were bad rumors about him.
At the End of the story, we see that Boo Radly saves Jem and Scout from dying when Bob Ewells try to kill or hurt them. I think they might think that he is now a good person and they might now think that he is a good person.