This story is told by the fisherman to the genie in the midst of the story "The Fisherman and the Jinni."
Duban is a sage (a wise man) who is truly remarkable in many disciplines. He can read Greek, Persian, Turkish, Arabic, Byzantine, and Syriac; he is skilled in botany, astronomy, and philosophy; and, most notably, he is a proficient healer.
His land's king, King Yunan, has leprosy. When Duban promises Yunan he can cure the condition without using even a tonic or ointment, the king insists that he begin right away. Duban creates a ball and mallet, and fills the mallet's handle with his special medicine. He then orders the king to play with the items; when Yunan does so, he perspires, and absorbs the medicine from the mallet handle into his bloodstream. After bathing and sleeping, Yunan is miraculously cured. Duban returns to the palace that morning to learn of his success, and then recites some celebratory couplets for the king.
Unfortunately, one of King Yunan's many viziers is an ugly, greedy and jealous man. When King Yunan's vizier notices the attention paid Duban, he hatches an evil plan to convince the king that Duban wants to poison him with an insidious medicine. It takes some persuasion, but the king eventually believes his vizier. He reasons that if Duban was powerful enough to heal him, he could certainly kill him in the same way.
King Yunan wants to punish Duban for this treachery, even though the physician has done nothing treacherous yet. When he and his vizier summon Duban to accuse him of malice, Duban protests, saying, "Spare me and Allah will spare thee; slay me not or Allah shall slay thee." The king is not to be persuaded, and order Duban beheaded.
Before the execution, Duban seemingly accepts his fate, and offers the king one of his prized books full of wisdom so that Yunan might heal himself should he grow ill again. The king obviously accepts, and opens the book once Duban is beheaded. (In some versions of the story, Duban promises his decapitated head will speak instructions for the book if some of his blood is placed upon it. Indeed, the head then speaks to the king through the final beat of the story.)
A few pages in, Yunan is confused to find there is no printing or words in the book. He continues to comb through it, separating the pages by wetting his fingers in his mouth, and thereby unknowingly absorbing the poison Duban had placed there. He quickly begins to die, realizing in his final moments that this is his punishment for killing the man who cured him, and that Duban was right when he said "Allah shall slay thee." (In versions where the head speaks, it addresses Yuban explicitly with this point.)
This story offers a very clear message: "Never bite the hand that feeds you." Though often relegated to cliche, it is an especially important lesson when one accepts the human tendency towards jealousy, greed, and blindness. The story warns us to be grateful for help offered to us, rather than push away or harm those who aid us. Further, it suggests that we are more susceptible to suspicion and distrust than we might hope. Had Yunan trusted in the sage's good intentions, rewarding the kindly man for his actions rather than punishing him solely because of suspicions, his tale would have ended differently.
In this most simplistic way, this story serves a very clear purpose for the old fisherman who is telling it in "The Fisherman and the Jinni." In that story, the fisherman rescues a genie who then insists on punishing the man for his help. This story offers a clear rebuke: if you do that, you are not only committing betrayal but might in fact bring down a greater vengeance on your own head.
But there is an outside force responsible for the rift between the king and Duban: Yunan's vizier. In this story, the cruel vizier serves as the principal antagonist, a catalyst for the conflict that escalates near the end of the tale. It is important that the vizier be described as evil and visually unappealing, because he needs to be separated from the other characters as much as possible. It would be too unsettling for an average person to cause such trouble; it has to be someone who has a history of bad intentions. And most intense of all, the vizier is known to be consumed by jealousy.
In this way, persuasion plays a key role in "The Vizier and the Sage Duban." We very often do not realize how susceptible we are to the persuasive words and actions of others; King Yunan certainly did not. The story suggests that we must endeavor to separate the influence of others from our own personal opinions whenever we are faced with a difficult decision, since we are so susceptible to baser ideas. The story deviates in its message, suggests we should trust others, but be careful not to trust too much. In short, we must nurture our own power of judgment, so we are not reliant on others who might have their own agendas.
And of course, the vizier was unappealing, and known to have vices. This is important, since it places some culpability on Yunan, who should have recognized his vizier's vices before trusting him. In other words, the story does not mean to suggest Yunan is simply a pawn to be pitied, but rather a man who obviously harbors his own jealousies and resentments if he was so easily fooled by a clearly ill-intentioned vizier. This complication serves two purposes. In the immediate sense, it suggests that we are never blank slates that can be persuaded, but in fact have our own prejudices that inform our decisions.
And in the larger sense, it is a message from the old fisherman to the genie. In that story, the genie had allowed his hatred of King Solomon to transform into a resentment against people who had not wronged him. Here, the old fisherman warns that we do ill by not checking our baser, uglier impulses and realizing them for what they are. As we learn when he lets the genie go free, the genie hears the lesson loud and clear. In an every larger sense, this inner branch story serves, as almost all the collection's stories do, as an implicit rebuke from Scheherazade to Shahrayar, who is abusing his power based on an irrational resentment against all women.