Realism of characterization basically refers to how real the author makes his/her characters, or the various methods authors use to create effective characters. It sounds like your instructor wants you to look closely and analyze what makes the characters in this book seem real. For instance, do they react differently to different people or situations much as real people do? Does Atticus treat his children the same way he treats his clients? Is it important that the characters in this piece seem realistic?
I hope this helps you get started.