Tate is referring to how, in a small way, Tom Robinson has been avenged. Tate doesn't want to bring Boo Radley, the real murderer of Mr. Ewell, out into the public eye for a trial. By simply covering it up by saying Mr. Ewell fell on his knife, Tate is able to protect Boo from public scrutiny as well as finally get justice for Tom's death. Tate is hoping to get Maycomb's peaceful ways of life back as soon as possible. Another trail concerning prominent Maycomb citizens will only stir things back up. By letting "the dead bury the dead" justice is finally served and more controversy is avoided.
Boo was the person who actually killed Bob and Boo has been in hidden for quite some while and he does not want Boo to come out in the public and be in trouble. He decided to cover it up and say that Bob fell on his knife and closed the case. Tate is trying to get the town of Maycomb calm and peaceful again and knowing the citizens, if Boo was involved it would only bring unhappiness. This is why he says let the dead bury the dead.