When Shakespeare deals with equivocation in Macbeth, he is featuring an issue that was current in his society. From the Norton edition of the play I learned that a Jesuit devised a particular theory of equivocation to use at his trial for his part in the gunpowder plot. Since the gunpowder plot was specifically designed to kill King James I, the reigning monarch when Macbeth was first produced, the use of equivocation in the play would have held special significance.
Though the witches, Macbeth, and the Porter are the primary uses of equivocation in the play, the theme is almost constant. Lady Macbeth twice talks to Macbeth about concealing his feelings and plots beneath a normal exterior, for instance, and Malcom suspects Macduff of playing falsely when Macduff comes to England to join Malcolm in the fight against Macbeth.
Well, an equivocation is a logical fallacy or something that constantly changes meaning depending on denotation. An equivocator is some who who does the above but also fails to make a direct statement. When the porter does his large speech on the play of the word "equivocation" and "equivocate," he is talking about liars lying. The character of the Porter is intended to create a catharsis after the murder of the King, yet while he is a funny drunkard, he is also expressing ideas that someone is lying and will continue to lie and put forth false pretense, misleading everyone. He is referring to what Macbeth will do.
Equivocation means to play with the truth by distorting it, to give a statement which is dubious and obscure, and is intended to conceal the truth or divert one from the path of truth.
In Macbeth, William Shakespeare has given many references to equivocation. The three witches instigate Macbeth's inner ambition and greed by luring him. And this they do through their so-called prophesies. The predictions of the witches and the apparitions are nothing but equivocations in the name of prophesies.
The witches, at first, tell Macbeth that he would be the Thane of Cawdor and the King of Cumberland soon. This is not something extra-supernatural they do, since, it is a matter of common-sense that, Macbeth, if he would have fought courageously and shown his man-of-the-battle attitude, he would definitely get rewarded, and if he continues to go after his ambition, would be the king possibly. Later, the apparitions prophesy that the no human born of women can kill Macbeth ever, and he would not be killed unless Birnam wood would come closer to his fort. The first prophecy is a lie in a sense that, Macduff who is born of his dead mother's body via surgery, kills him. The second one is an equivocation also, since, though Birnam Wood does not come closer, yet the soldiers of the opposition hide them under the leaves of the forest, and this makes him think as if the forest itself is moving towards him, and he loses all his hope and courage to fight further. It is clear hence that, what the prophecies told was half-truth to destroy Macbeth.
These are some references to equivocations used in Shakespeare's Macbeth. The equivocations are highly related to the theme of illusion in the play.