Both Scout and Jem have certain fears and beliefs, mostly stemming from their youth, and the naivety that comes along with being children. There are two main people that demonstrate their fears and prejudices--one is Boo Radley, and the other is Mrs. Dubose.
Jem and Scout, being impressionable children, believe all of the rumors and hype that float around the town about Boo Radley. Boo, really Arthur, is a very kind-hearted man who is greatly misunderstood by society. He is rumored to be a "malevolent phantom" who lurks about the town at night, peeping into people's windows, slicing people up with scissors, and committing crimes and atrocities. Jem, Scout, and even Dill fall prey to these rumors, and become fascinated with the stories, daring each other to touch the house, drop notes to Boo, and peek in windows.
By the end of the novel they learn the real truth, which is that Boo is a kind man who has attempted to reach out to them, make friends with them, and who ultimately risks his own life to save their own. They learn the valuable lesson that sometimes, people are not as they seem, and that one should never judge another person, especially if they are ostracized by society, until you get to know them.
The other person that teaches them a lesson on prejudices is Mrs. Dubose, the surly old lady that shouts at them whenever they go into town. They can't stand the old lady, and, it's hard to not blame them. She has an acidic, vicious tongue, and she leaves no one unscathed, even Atticus, their father. However, as they go each day to her house to read, they see just how physically ill she is, and Atticus informs them of her battle to overcome her morphine addiction, calling her a "lady" and one of the most "courageous" people that he knows. Jem, even though he might not appreciate it at the time, is learning once again that people are not who they seem, and that until you get to know them, you should withhold your judgment.
Jem and Scout also hold some rather naive beliefs about life and people; they believe that they live in a world where the innocent go free, where right always reigns, and where people are always good and full of integrity. The Tom Robinson trial teaches them that these beleifs are unrealistic and idealistic, unfortunately. They learn a lot from his unfair conviction and death, and from how people behave during the entire ordeal.
I hope that these thoughts helped; good luck!