The passage implied in the question is found in Chapter 25:
Atticus had used every tool available to free men to save Tom Robinson, but in the secret courts of men's hearts Atticus had no case. Tom was a dead man the minute Mayella Ewell opened her mouth and screamed.
The contrast here is the one that exists between the legal principles upon which the system of justice is based and the human weaknesses and prejudices that can corrupt the dispensing of justice in court. In court during Tom's trial, Atticus defended Tom within the legal system and, in fact, proved beyond any doubt Tom did not commit the crime he was accused of committing. However, because of the racist culture of Maycomb, the presumption of innocence was never extended to Tom. He was "convicted" in people's hearts before he ever came to trial. Because he was a black man in Maycomb, he was presumed guilty as soon as he was accused by a white woman. In the "secret courts of men's hearts," no evidence was necessary beyond the color of Tom's skin. Minds were closed, and this public opinion was instantaneous.