In act 2, scene 2, Macbeth uses the word "sleep" eight times. Describing the murder of King Duncan, he tells his wife that he heard a voice:

cry "Sleep no more!
Macbeth does murder sleep," the innocent sleep,
Sleep that knits up the ravell'd sleeve of care.

Lady Macbeth asks him to explain what he means, and he replies:

Still it cried "Sleep no more!" to all the house:
"Glamis hath murder'd sleep, and therefore Cawdor
Shall sleep no more; Macbeth shall sleep no more."

The voice that Macbeth hears is likely the voice of his conscience. It tells him that he will no longer be at peace or be able to rest now that he has committed such a grievous crime.

He has murdered his king for no better reason than to satisfy his own ambitions and greed for power. He has also killed three people in their sleep—when they were unable to defend themselves. This makes what he has done a dishonorable, cowardly act. And because he has done all this he has also, metaphorically, murdered his own chances of ever being at peace again, either with himself or with the world.

For much of the rest of the play, Macbeth tries to eliminate all possible threats to his power in a vain attempt to find peace. He thinks that once he has eliminated every threat he will finally be able to sleep—or be at peace—once more. In act 3, scene 2, he talks about "the affliction of these terrible dreams" that keep him awake at night. For this reason, he orders the murders not only of Banquo and Macduff but also of their young children.

The mistake he makes is to assume that his sleeplessness is because of the threats, imagined or real, posed by his enemies. He doesn't realize that it is his conscience that makes him restless and denies him sleep. This is why, no matter how many threats he eliminates, he remains restless and haunted.