There are two types of relationships that create conflict and tension in To Kill a Mockingbird. Relationships between family members create conflict. Tension is also caused by relationships between different members of Maycomb society.
There are conflicts between Jem and Scout, and between the children and their father. Any family has tension, and the tension between Scout and Jem is mostly based on Jem being older than Scout and having a better understanding of the way the adult world works than she does. Tension between Atticus and his children is also caused by his choice to defend Tom Robinson, a choice that causes problems for both of his kids and one that they do not fully understand until the trial. Another example of family conflict is Aunt Alexandra, who has conflicts with Scout over what it means to be a lady.
There is also tension and conflict caused by relationships between Atticus and other members of the Maycomb community due to Atticus’s defense of Tom Robinson. Atticus is normally well-respected in Maycomb. His high standing in society is maintained even throughout the trial, because people respect his choice even if they disagree. However this puts Atticus at odds with various members of Maycomb, such as the incident with the Cunningham mob. If Atticus had no relationships with these people to begin with, then the tension would not be so high.