It's notable that Macbeth says these lines to himself. He doesn't want anyone to know about his ambitions, least of all Malcolm, whom Macbeth frankly acknowledges he'll have to step over if he's to become king. So anxious is Macbeth not to show his hand that he wishes that the stars would hide their light so as to cloak him and his ambitions in a pall of darkness.
Macbeth exaggerates, of course. But the essence of what he's saying makes perfect sense. Macbeth is worried that his overriding ambition to be king will become obvious to those around him, and that's the very last thing he wants.
Though fiercely ambitious, Macbeth still feels more than a hint of unease at what he has to do to fulfill his ambitions. If Macbeth is to become king, then Duncan will have to die, and his murder will not be pretty. In fact, Duncan's murder will be so unpleasant that Macbeth resolves not to look at his evil handiwork.
But Macbeth will do it anyway. If he wants to become king—and he most certainly does want to be king—then he has no choice; he must kill Duncan. His hands will still perform the dirty deed even if he can't bring himself to look at it.
Further Reading
Macbeth speaks these words in act 1, scene 4, and they represent an early step on his journey towards all-consuming ruthless ambition and villainy. Duncan, the current king, has just announced that his son Malcolm will be his heir. This makes Macbeth feel uneasy because, of course, he has been told by the three witches that he will actually become king of Scotland. Thus, seeing Duncan name his own son heir makes Macbeth worry that others will realize what is going on in his head. Macbeth is thinking that whatever Duncan says, Malcolm cannot possibly be king, because Macbeth will be king.
When Macbeth utters these lines near the end of act 1, scene 4, he has just learned that the king, Duncan, has named the king's own son, Malcolm, as his heir to the throne. Because of what the witches told Macbeth about becoming thane of Cawdor and king, and the fact that he was rewarded with the former title just moments later, Macbeth seems to have felt it very likely that he would be named Duncan's heir. He now realizes that he will not be named the prince of Cumberland, and so that is "a step / On which [he] must fall down or else o'erleap." In other words, he must stop his thoughts about becoming the king here and now, or he must come up with some other way to accomplish it.
Macbeth tells the stars to "hide [their] fires" so that no one will be able to look at him and "see [his] black and deep desires" to become king. He wants the throne, to have that status and power, and he knows that this desire is bad, because it means that he will have to displace someone else to obtain what he wants: either Duncan, or Malcolm, or both. The final two lines of this speech are a bit more difficult to understand. What they mean is that Macbeth does not want to see what his hand will likely have to do (kill Duncan) in order for him to become king. He is not murderous and takes no joy or pleasure in the thought of murdering his king, cousin, and friend but, rather, feels fearful at the idea of what he feels compelled to do.
Stars hide your fires; Let not light see my black and deep desires: The eye wink at the hand: yet let that be. Which the eye fears, when it is done to see.
In Macbeth Act I, Scene four, Macbeth speaks of his "black and deep desires." Only earlier had Macbeth wondered about the witches' prediction that he gain control of the cawdor; he now wonders if their prediction concerning the kingship might also prove true. Macbeth instructs the "stars [to] hide your fires," because he wants his secret yearning for the throne to remain covered in darkness, especially the fact that he would be willing to do anything, including murdering Duncan, the rightful king, to achieve his ambition.
In addition to the stars hiding their light to cover Macbeth's desires in darkness, Macbeth would also have his "eye wink at the hand," meaning that his eyes would be blind to the actions of his hands. Macbeth himself does not want to see what he must do to achieve the throne, but at the same time, he urges "let that be what the eye fears, when it is done, to see." This statement suggests that even though he does not wish to see what must happen, he desires the end result, the throne, all the same.
Ultimately, these four lines of Macbeth's reveals two important considerations of his character:
1) Ambition--He wants the throne very badly, but does not want anyone to know how far he would be willing to go in order to achieve it.
2) Cowardice--He does not want to have to face the reality of the consequences of his action. He fears what he must do, like murdering Duncan, but still wants his death and the throne all the same.