Why is "...in the secret courts of men's hearts Atticus had no case." relevant with repsect to the theme or symbolism in this book?

The "secret courts of men's hearts" refers to their prejudice.

Social Inequality

Along with struggling with concepts of good and evil, Scout and Jem spend a great deal of time trying to understand what defines and creates social strata. Scout tends to believe that "folks are just folks", while Jem is convinced that social standing is related to how long people's relatives and ancestors have been able to write.

Scout elucidates the town's social strata quite clearly on her first day at school when Walter Cunningham does not have lunch or lunch money. Her classmates ask her to explain to the teacher why Walter won't take a loaned quarter to buy lunch, and she lectures the teacher on the Cunningham's financial situation and how they trade goods for services. Scout and the other children have a very clear understanding of the social inequalities in their town, but see these inequalities as natural and permanent. The Finch family falls rather high up in the social hierarchy, while the Ewell family falls at the bottom. However, this hierarchy only includes white people. Maycomb's black population fall beneath all white families in Maycomb, including the Ewells, whom Atticus labels as "trash".

Scout understands this social structure, but doesn't understand why it is so. She believes that everyone should be treated the same, no matter what family they are from. For instance, when she wants to spend more time with Walter Cunningham, Aunt Alexandra objects saying no Finch girl should ever consort with a Cunningham. Scout is frustrated by this, as she wants to be able to choose her own friends based on her definition of what makes a good person: morality.