That scene takes place in Chapter 30. Jem and Scout have been attacked by Bob Ewell on their way home from school after the Halloween play. Jem's arm was broken, and he is unconscious. Boo Radley comes to their rescue, carrying Jem into the house. The sheriff, Heck Tate, is called. When he investigates, he finds Bob Ewell dead under the old tree, with a kitchen knife stuck in him.
There follows an argument between Heck Tate and Atticus. Heck keeps insisting that "Bob Ewell fell on that knife and killed himself." This is his proposed cover-up. Atticus says, "Nobody's hushing this up. I don't live that way."
Atticus is refusing to hush the matter up because he thinks that it was Jem who stabbed Ewell, in self-defense. If Jem has killed a man, Atticus wants the matter brought out into the open and settled, or the rumors of it will haunt Jem for the rest of his life. Also, Atticus feels that he can't let his children see him agree to spread a falsehood. This would undo everything he's been trying to teach them. "If they don't trust me they won't trust anybody."
Heck Tate, though, has realized that it wasn't Jem who stabbed Bob Ewell. It was Boo Radley.
When it finally dawns on Atticus that the one who stabbed Ewell was not Jem, but Boo, he feels differently about hushing the matter up. Jem is just beginning his life and he needs a clean record and a solid foundation of integrity on which to go forward. But Boo is a shy, reclusive man who hasn't been outside of his house in years. Public scrutiny would destroy him.
Atticus is still bothered by the need to lie about what happened. He is worried that his children will lose respect for him, and for the value of truth. But Scout assures him that she understands: outing Boo Radley would be "like killing a mockingbird."