Just to add a few comments to the answer above.
One of the most important aspects of King's letter is his tone of respect for and conciliation with the clergymen who criticized his intervention in Birmingham. Even though King felt that he had been unfairly attacked by people who did not fully understand the issues involved, not just in Birmingham but in the struggle for civil rights in general, King very skilfully reminds these men that they and he are trying to reach the same goal:
But since I feel that you are men of genuine good will and that your criticisms are sincerely set forth, I want to try to answer your statements in what I hope will be patient and reasonable terms.
King establishes a respectful but forceful tone here by acknowledging that he is responding to men of "genuine good will" and, more important, that his response will be set forth in "patient and reasonable terms," a commitment he keeps by going through, very patiently, the history of Birmingham's struggle and its relation to the larger struggle for civil rights. Every paragraph that follows this is a masterful exercise of passion and logic.
After having discussed the civil rights struggle in detail, King carefully draws his opponents into his circle by reminding them that
My friends, I must say to you that we have not made a single gain civil rights without determined legal and nonviolent pressure.
King's statement is not merely a point of rhetoric--his point here would have resonated with his critics because it is manifestly true, and even his critics would have recognized the reasonableness of this truth. And King has subtly reminded his critics that they are, despite their views, his friends.
At several points in the Letter, King reinforces his reasonable tone by acknowledging the validity of his critics' concerns about the violence in Birmingham:
You express a great deal of anxiety over our willingness to break laws. This is certainly a legitimate concern.
His tone here is conciliatory and respectful of the clergymen's fears about the violence that King's non-violent resistance has sparked, but he puts them at ease by acknowledging the reasonableness of their concern. King maintains own tone of reasoned disagreement throughout the Letter.
Later, when King writes of his disappointment with the "white moderate" who fails to understand the need for increasing action against those who are committed to segregation, King again subtly reminds his critics that they are bound by the convictions of their religion:
I must make two honest confessions to you, my Christian and Jewish brothers.
Again, King encircles his critics with respect and, more important, with their commonality: they are all men of religion who, despite their different view of tactics in the struggle for civil rights, are "brothers." His use of the word "confessions" is also masterful because it carries both religious overtones, as well as establishes a sense of intimacy. No matter how much King and they disagree about how to achieve civil rights, King uses every opportunity to point out their relationship as men of God, which carries his overall tone of respect and reason to the end of the Letter.
Letter from Birmingham City Jail is a call to unity. Dr. King addressed the letter to several clergyman, who had written an open letter criticizing the actions of Dr. King. Dr. King tells the clergymen he was upset about their criticisms. They claimed Dr. King is an outsider and has no place in Birmingham. Dr. King goes on to tell them, that the SCLC is based in Atlanta, but runs throughout the south. He goes farther to tell them he was invited to speak in Birmingham, and that is why he is there.
He goes farther with this, by telling them he has a moral issue for being there. The battle of injustice has brought him here. He states that all communities and states are are interrelated. He feels compelled to work for justice anywhere injustice is practiced. He goes into detail about how he has organized non-violent protests.
Dr. King then goes on to tell of how the black man has struggled for so long. He says the black man has waited for more than 340 years for justice. He gives comparisons to help the reader understand not only the historical reasons why segregation is wrong, but the costly emotional effects that it has on everyone who experiences it. His terminology creates a clear definition between the whites and blacks, as the segregator and the segregated.
His use of comparison makes the African-American's plight of segregation seem almost holy. He compares himself to the Apostle Paul and his "gospel of freedom" to the Gospels of the eighth century prophets. He goes on to talk about the emotional sufferings of what the blacks went through. The police brutality, lynching and the drownings that the blacks had gone through, are detailed.
Dr. King's use of comparison-emotional tools, contrasting terminology all help the reader understand the real meaning behind civil disobedience and the horrible fault in segregation. Dr. King's way with words makes his writings almost poetic in nature. His writings are still so prevalent in this day and age as well. His words will live on forever.