There are at least two important conflicts in To Kill A Mockingbird: One concerns the perception of the mysterious Boo Radley, which is the dominant conflict of the first half of the novel; and the second centers on the trial of Tom Robinson, which dominates most of the remainder of the book.
Boo Radley is an outcast to both the town and his own family, who keeps him hidden away in their rambling, old house. While most everyone in the town, including Atticus, choose to leave poor Boo alone--partly out of fear of the unknown and partly out of a misguided respect for privacy--Jem and Scout make it their goal in life to bring him out into their world and make him their friend.
Meanwhile, the rape trial of the honest, God-fearing Tom Robinson takes precedent midway through the novel. To most of the Maycomb citizenry who are not on the jury, and to probably nearly every reader of the novel, it is clear that Tom is telling the truth when he defends himself against the charge of rape brought by Mayella Ewell. But Tom is black, and Mayella--despite coming from the most reviled family in town--is white, and as Atticus knows from before the trial even begins, Tom will be found guilty.
This conflict between Tom and Mayella spills over to include her father Bob Ewell, whose hate for Atticus--Tom's defender--is so strong that he decides to take revenge against the Finch family in a most despicable manner.
Atticus has to choose whether to tell the entire truth of what happened. Boo killed but he did it to save children. On the other hand, if Atticus keeps quiet and goes along with the ficticious story of what happened, then he can protect Boo. Boo cannot handle the ramifications if the truth gets out. However, Atticus is an honest man. Should he hide the truth or tell the whole truth and risk having a man's life destroyed. This is the main conflict. Is the whole truth worth telling if it hurts everyone involved ? Remember what he said about not hurting the Mockingbirds. Is Boo a Mockingbird ?