This reference comes in Chapter 25 during the trial case of Tom Robinson. In spite of the impressive defence that Atticus makes of Tom Robinson, and the way that he effectively proves that he was not guilty of the crime of rape, Scout shows just how much she has grown up since the beginning of the book with the following quote:
In the secret courts of men's hearts, Atticus had no case.
Although the evidence that Atticus has brought before the court effectively clears Tom Robinson, Scout draws the reader's attention to the "secret courts" that lie within people that are not so easily swayed by logic and proof. These "secret courts" are impacted by concepts such as prejudice and racial discrimination, and this is something that dictates the response of the court above all else. Therefore, Atticus took the case and defended Tom Robinson even though he knew that the racial prejudice in Maycomb would never allow Tom to be acquitted, in spite of his obvious innocence. The "secret courts" therefore refers to the prejudice and attitudes that exist within humans and how they decide on somebody's guilt or innocence without reference to the truth.