In the ending chapter of "To Kill a Mockingbird", Atticus and Mr Heck Tate (the Sheriff) are deciding who is responsible for the death of Mr Ewell. Atticus thinks Jem killed Mr Ewell but Heck knows it was actually Boo Radley. Heck Tate said that instead of bringing Boo to the public they should just "let the dead bury the dead." What is meant by this quotation?
In the book In To Kill a Mockingbird, Boo Radley (The one who killed Bob Ewell) and Tom Robinson are seen as "mockingbirds".
Atticus said previously in the book that it is "wrong to kill a mockingbird as they do nothing for us other than sing their hearts out". Heck Tate realizes that Jem didn't kill Bob Ewell but it was in fact Boo Radley.
Heck already saw one innocent man have his life ruined because of the community (Tom Robinson). Tom was killed because of pure racism and hatred in the white society and Heck knew that if the whole of Maycomb were to know Boo Radley killed Bob Ewell everyone would come and thank him and bring presents etc. Heck realizes that Boo does not like this kind of attention and he killed Bob Ewell out of pure kindness.
Heck stated "let the dead bury the dead". He states that they should just say Bob Ewell fell on his knife while drunk and killed himself, but what he actually means is that we should let Tom Robinson (a man who was innocently killed) bury the dead (Bob Ewell, the man who played a massive part in the death of Tom Robinson). It is also a quote from Luke 9:60 in the Bible.
It might also be that Heck feels that Bob Ewell's death cancels out the death of Tom Robinson.
Even Scout the little girl realizes that its wrong to put Boo in the spotlight as she said to Atticus "well Atticus, its a bit like shooting a Mockingbird" hence the title of the book. "To Kill A Mockingbird", the mockingbirds in this book are all those who are persecuted by society as a "malevolent phantom" (Boo Radley) or as a "negro" (Tom Robinson) are Mockingbirds because Tom and Boo has done nothing other than help the community. Some other Mockingbirds might be Mayella Ewell who is abused by her father and forced to look after the many kids in her house to only get beaten by her father and forced to testify "rape" against Tom.
"Let the dead bury the dead" is an old expression which originates from the New Testament. When a man wished to follow Jesus and become a disciple, he asked if he could first bury his father, who had just died. But, Jesus replied,
Let the dead bury their own dead, but you go and proclaim the kingdom of God [Luke 9: 59-60]
This response's meaning is that the man must not put earthly duties before spiritual ones. After the children are attacked by the reprobate Bob Ewell and Jem left arm is seriously injured, Atticus discusses the matter with Sheriff Tate, alluding to Jem's having to go to court and testify to what has occurred.
"Mr. Finch, do you think Jem killed Bob Ewell? Do you think that?"
In the ensuing argument between the two men, Heck Tate explains that Bob Ewell fell upon his own knife because he disbelieves what Atticus proposes, that Jem stabbed Ewell; furthermore, he sees no need to involve Jem in this matter of the death of the despicable Ewell. The honorable Atticus does not want Jem to lose respect for his father if he covers the truth for his son. But, Tate insists on giving his report of the incident. He tells Atticus that this is his town, and he knows everything that goes on.
There's a black boy dead for no reason, and the man responsible for it's dead. Let the dead bury the dead this time, Mr. Finch. Let the dead bury the dead."
In other words, let Tom Robinson "bury" Bob Ewell as an act of poetic justice, and the incident will be taken care of; in this way, Boo Radley with his "shy ways" will not be exposed to the gossip and cruelties of the public. The town can "move on" from the repercussions of the trial as all the injustice connected to it will finally end. The dead will take care of the dead, and the living will go on living in their own ways. Otherwise, it would be like killing a mockingbird to bring Boo to court.
Atticus finally understands the wisdom of Sheriff Tate and agrees with him.
There is also an implication that the dead are dead and nothing can be done for them, so the living should continue with their lives and more worthwhile endeavors. In this case, allowing Boo Radley to not be drawn into the spotlight.
"Let the dead bury the dead." No doubt Harper Lee heard that verse all her life. In the Gospel of Matthew, Jesus says it to shame a new disciple who wants to bury his father. In those days, however, "burying" included a year after the original interment for the bones to become bare, upon which they would go into a tomb. So the disciple is trying to postpone his invitation for as much as a year.
What does that have to do with Ewell's death? Not much. Tate and Finch argue over how Ewell died. Finch, the lawyer, wants to have a trial and get at the truth, even if it implicates his daughter. Tate is tired of the whole business, and another trial will keep the town on edge. The simple and obvious solution is that Ewell, drunk and in the dark, fell on his own knife. Tate invokes the ultimate authority, the Bible, and quotes Matthew, hoping that will settle everything.
What Tate probably means is "What's done is done" or "let sleeping dogs lie" or a confusion of both. He's seen too much death recently. He can hold an inquest, rule Ewell's death an accident, and let everyone move on.
I have always understood the phrase "let the dead bury the dead" to mean "let it go, it's over, time to move on". In the case of "to Kill a Mockingbird" that is exactly what Sheriff Tate is telling Atticus. No earthly good can be served by arresting Boo Randall for killing an evil man who was trying to kill a child. All it can do is cause more harm. So bury the truth and let the dead deal with it.