Mr. Cunningham is the father of Walter Cunningham Jr, Scout's classmate. He's also a client of Atticus's, and pays Atticus for his services in goods rather than money, because that's all he can afford. In the eyes of Maycomb, the Cunninghams are a step below the townspeople (they're poor farmers), but a step above the Ewells (they eke out enough to survive from the land rather than going on welfare).
Mr. Cunningham, along with others like him, is part of the mob that tries to lynch Tom Robinson the night before the trial, putting him on the side of regressive and prejudiced values. When Scout talks to him about his son, however, he turns back and takes the rest of the mob with him. At the trial, Mr. Cunningham's double first cousin is the only one willing to acquit Tom. Mr. Cunningham and his family suggest that at least some kinds of discrimination and violence come out of ignorance, and that experience can open eyes and change minds.