What is the dramatic significance of the quote, "It will have blood, they say; blood will have blood" (Act III, scene iv)?
In an interpretive manner, "blood will have blood" (3.4) is a double-meaning word-play (different from a double entendre because the latter has a hidden offensive or sexual meaning). Its first meaning is in reference to the predictions of the three witches in Act 1, scene 3, who have told Banquo that his "blood" will have "blood" (sons)--"Thou shall get kings, though thou be none" (1.3)--while the second meaning is that the shedding of Banquo's blood will have to lead to (get) the shedding of his sons' blood as well, because the prediction was that Banquo should be the father of kings, which Macbeth can't allow.
When Macbeth utters these words, he uses the phrase more in this second meaning; his bloody path of murder must lead to other murders. Having killed Duncan and become king, he must now eliminate Banquo and his progeny to ensure that he remains king. This idea, too, is in line with the Elizabeth Chain of Being: whatever affects one thing affect others. Thus, there is an interconnection of one bloody deed with another. In fact, Macbeth even alludes to the sons of Duncan earlier in Act 3, scene 1, with the word "bloody":
Macbeth: We hear, our bloody cousins are bestow'd
In England and in Ireland, not confessing
Their cruel parricide, filling their hearers
With strange invention:... (3.1)
This quote from Act III, scene iv, is said by Macbeth when he sees the ghost of Banquo at his feast. Its significance lies in the fact that Macbeth is beginning to have a guilty conscience (or at least is fearful of what will happen to him because of his actions) concerning the murders he has committed - first the murder of King Duncan, then the murder of his former friend, Banquo. Banquo's ghost coming to Macbeth causes Macbeth to act insane and irrational in front of his wife and guests, and Macbeth states that the blood he has shed will come back for revenge on him - blood will have blood.
This quote and scene in particular are both turning points in the behavior and mental state of Macbeth. So far, he's committed some terrible acts with some guilt, but he is still able to function. He feels guilt after the murder of Duncan, but the act functions as the releasing of a dam - following it, he finds himself committing even more terrible sins, like the murder of his friend Banquo.
In this scene and with this quote, the reader sees that Macbeth is feeling both guilt and paranoia. The fact that he sees the ghostly body of Banquo at the table shows how distracted he is by the thought of his friend and also the disintegration of his mental health. This quote show us how paranoid he truly is. He is anticipating further turmoil because of his actions - literally, the blood of Banquo demands further blood, either his own or others.
Macbeth has murdered King Duncan, Banquo and now plots to kill Macduff. He has spilled alot of blood in his hands, and if he must die while fighting for the right to his throne, then "blood will have blood". He will not give up the throne without a fight!