The motif of sleep is so prevalent in Macbeth because sleep is symbolic, both of death and of peace of mind. Many of the characters, especially Macbeth, have trouble sleeping.
Nightmares can also serve as foreshadowing devices. Banquo has nightmares about the witches, and his fears are later realized.
It is no coincidence that Duncan goes to Macbeth’s castle to sleep. In Act I, Scene 7, Lady Macbeth compares sleep to death (p. 24). They plan to use the guards’ sleep to sneak into Duncan’s room and murder him.
It is ironic that Duncan is murdered in his sleep when Macbeth heard a voice say “Macbeth doth murder sleep” and he describes sleep as “innocent” in Act 2, Scene 2 (p. 30). When Macbeth imagines he hears a voice cry out “sleep no more” he is feeling uneasy. He is concerned about the plans to murder Duncan.
Lady Macbeth’s famous sleepwalking scene demonstrates her lack of peace of mind. She cannot get any rest, because she feels guilt over Duncan’s murder (not to mention the other murders her husband committed after she turned him into a homicidal maniac by convincing him to kill Duncan).
Yet who would have thought the old man to have had so much blood in him? (Act 5, Scene 1, p. 77)
Lady Macbeth’s sleep is troubled by visions of Duncan’s blood, just as Macbeth’s guilt troubled him earlier. Macbeth also begins to lose his mind because of his guilt. He compares life to a “brief candle” easily put out.
Tomorrow, and tomorrow, and tomorrow
Creeps in this petty pace from day to day
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. (Act 5, Scene 5, p. 84)
In the end, life is meaningless, “full of sound and fury, signifying nothing.” In the end, all we have is death: the endless sleep.
After realizing that he had committed an unspeakable act by killing his king and kin, Duncan, Macbeth says that "Macbeth has murdered sleep, Glamis will sleep no more". In fact that is exactly what happens...Macbeth's guilty conscience does not allow him to rest and eventually leads him down the path of insanity.
Lady Macbeth also suffers guilt because of her role as an accomplice to Duncan's murder. One might say she was actually the instigating force behind Duncan's murder. Her guilt manifests itself in her sleepwalking and her excessive rubbing of her hands to try to remove Duncan's imaginary blood. The inability to sleep leads Lady Macbeth to commiting suicide.
It's never actually specified that she kills herself.