Atticus is speaking about the integrity of the courts when he refers to the "great levelers". He means that in the courts, every man should be able to perform on a "level playing field", and have a fair chance of winning.
Atticus makes this statement in his closing arguments before the jury in the Tom Robinson case. Tom Robinson is a black man accused by a white woman, and although the evidence shows that he is clearly innocent, Atticus knows that the truth has little chance of being upheld in Maycomb County because of an atmosphere of racial stereotyping and prejudice which goes back for generations. Still, Atticus makes this final appeal before the court, reminding all present that no matter what conditions may exist in communities at large, men should be judged as equal at least in the courts. Atticus says,
"there is one way in this country in which all men are created equal - there is one human institution that makes a pauper the equal of a Rockefeller, the stupid man the equal of an Einstein, and the ignorant man the equal of any college president. That instituti0on...is a court. It can be the Supreme Court of the United States or the humblest J.P. court in the land, or this honorable court which you serve. Our courts have their faults, as does any human institution, but in this country our courts are the great levelers, and in our courts all men are created equal" (Chapter 20).