The quote is found in Act ll, Scene 1, and is a monologue by Macbeth on his way to commit his pernicious deed, regicide. He previously expressed doubt about killing Duncan, but was persuaded by his wife to complete their plan. Macbeth is overwhelmed by the commission of his dreadful task, and thus imagines seeing a dagger floating ahead of him, leading him to Duncan's chambers.
Macbeth's continuous reference to the dagger and his imagined vision that it is changing to a bloody object for assassination means he is intensely disturbed by the magnitude of the crime he is about to commit. He cannot decide whether the dagger is real or imagined. It looks exactly like the object he is about to use to assassinate the king. To make sense of its appearance, he rhetorically asks if it is a "false creation proceeding from the heat-oppressed brain," which means he is acutely aware of the turmoil in his mind. One can assume that he is not truly ready (or even prepared) to proceed, but he has made a pledge and thus feels committed.
In addition, the persistent appearance of the dagger seems to urge Macbeth to move forward. It is obvious that he wants to erase the image, but it does not fade, and he states that his eyes are overwhelmingly focused on it. His other senses are dominated by what he sees. The image is enhanced, and Macbeth tries to convince himself that it does not exist and has been brought about by "the bloody business," as he calls it.
Macbeth concludes that, at this particular time, half of the world "seems dead," giving evil an opportunity to reign, unbounded. It is at this time that witchery is afoot and malice is committed. Those sleeping are troubled by wicked dreams. He alludes to Hecate, queen of the witches and the rapacious Tarquin, a Roman king, who used the veil of night to commit his evil. Macbeth, in effect, is referring to himself, who "towards his design moves like a ghost."
As a consequence, he calls on the earth to be deaf to his movements, since he fears its very stones might announce his whereabouts and thus betray his evil purpose. He encourages himself by stating that as long as he only threatens to kill Duncan, the king continues to live. He ends by stating that he must put his words into action, otherwise the desire to act will grow cold and the obstacle to his overriding ambition, Duncan, will not be removed.
Symbolically, Macbeth's monologue represents the pervasive theme of evil, accompanied by the supernatural. The first scene of the play illustrates this fact when the audience is introduced to the witches performing a ritual and plotting their meeting with Macbeth. This atmosphere of perfidy and the abnormal is accentuated throughout the drama, and we are constantly reminded of its presence. We see it in Macbeth plotting Banquo's murder, arranging the murder of Macduff's family, seeing Banquo's blood-soaked ghost at the banquet table, visiting with the witches, and seeing the apparitions which they conjure.
Secondly, the monologue symbolizes Macbeth's initial fear of committing a reprehensible deed. Although Macbeth is used to slaughter and mayhem on the battlefield, this is so much greater and more personal. He is overwhelmed by the magnanimity of what he is about to do and is, therefore, in torment. He has to take the life of a relative, someone he respects and is supposed to protect and defend. That, surely cannot be easy.