Sleep is something that we all need in order to survive. We sleep to rest and rejuvenate ourselves, and we need to feel safe in order to get a truly restful sleep. When Macbeth "murders" sleep, he makes it into something that is no longer safe to do. He has taken away something that we take for granted, he has not only destroyed innocence, he has also taken away safety, sanctity, and security. Sleep is also a time of dreams, and we want those dreams to be good, but Macbeth has turned dreams to nightmares, taken is into the evil that we fear in the darkness, and made it such that if we close our eyes we are likely to see bad visions instead of having peaceful dreams.
Sleep heals, it nourishs, and is representative of life itself. For an excellent analysis of this line, see Bill Long's commentary:
Three things about sleep should be noted: (1) Sleep as the great interpreter of life; (2) Sleep as healer; and (3) Sleep as nourisher. Each calls for comment.
(1) I don't suppose that anyone has written a more eloquent line in English about sleep than in l. 36--"Sleep that knits up the ravelled sleeve (sleave) of care." Something that is ravelled is "tangled, confused, involved" (OED) or "frayed out; with frayed edges; ragged." A "sleeve" is a part of a garment or "a slender filament of silk obtained by separating a thicker thread." Finally, the word "ravel" not only suggests the reality of tangledness or confusion, but was a kind of medieval bread ("ravel bread"), of flour with the bran left in, which may connect the "ravelled" sleeve of care with the "nourisher" in the last line above. In any case, the principal picture communicated here is that sleep "knits up" or secures what has become confused or tangled in our lives. It brings lose ends together, tightening them and producing an untangled sleeve or garment. This is what I call sleep's interpretive capacity. It lets things settle, it suppresses some of the insistent voices that rang in our ears and lets others come to the fore, it smooths out what was so ragged or bumpy in our minds before we went to sleep. Christian hymnody might say "God is the great Interpreter, and he will make it plain," but Shakespeare knows better: sleep is the bread and wine of the common grace available to all creatures.
(2) Sleep also heals. It is "sore labor's bath/ balm of hurt minds." The bath and the balm, residing next to each other in the text, make us stop and bathe in the words. The body and mind are oppressed and stretched by the work of the day. Labor is sore in two senses: it creates conflict between people and it results in bodily infirmity and pain. But the mind also becomes overwhelmed by the bruising realities of life. Sleep not only interprets life, giving us mental clarity as we approach the next day, but it gives the mind and body peace and healing with which to rise and return to the battle.
(3) Finally, sleep nourishes. It gives us that extra meal that adds no calories, the feast that produces no waistline gain. And, Shakespeare calls it the "chief" nourisher in life's feast. One might want to quibble with him. Why not sex? Why not the blessings of friendship? Why not the inner satisfaction derived from seeing children successfully negotiate life's rapids? But sleep is offered to us each day, a gift that beckons and rewards; that nourishes and heals.
Sleep, or the lack of it, is a prevalent theme in Shakespeare's Macbeth.
As Kenneth Muir points out in "Image and Symbol in Macbeth," found in A Norton Critical Edition of the play (254-266), the first mention of the theme of sleep in the play is made by the First Witch:
Sleep shall neither night nor day
Hang upon his penthouse lid. (1.2.20-21)
She curses the Master of a ship, because his wife slights her. After Macbeth and Lady Macbeth assassinate Duncan, they
In the affliction of these terrible dreams
That shake us nightly;... (3.2.19-21)
In contrast, King Duncan, once dead, "sleeps well" (3.2.25). And, says Muir:
An anonymous lord looks forward to the overthrow of the tyrant, when they will be able to sleep in peace. Because of 'a great perturbation in nature' [5.1.8.], Lady Macbeth
is troubled with thick coming fancies
That keep her from her rest. [5.3.39-40]
But the key passage concerning sleep is the one you ask about:
Methought I heard a voice cry "Sleep no more!
Macbeth does murder sleep," the innocent sleep,
Sleep that knits up the raveled sleeve of care,
The death of each day's life, sore labor's bath,
Balm of hurt minds, great nature's second course,
Chief nourisher in life's feast-- (Act 2.2.38-43)
Thus, sleep becomes insomnia, with the dead Duncan the only figure in the play capable of sleeping. Even the drunk, comic Porter's sleep is interrupted, once the deed of assassination is done.
As much as sleep symbolises a great deal of things, the most direct interpretation would come from the fact that Macbeth murdered Duncan in his sleep, in his most peaceful state of mind. It is definitely cowardice to attack from the back.
Because of this heinous sin he committed in someone's sleep, Macbeth has lost of his peace of mind and could not sleep feeling safe. His conscience pricks him hard and reminds him of his sin.
Hope this helps :)
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I shall add my own few lines to the above answer as that already seems adequately long and detailed to me. And, I'd like to remain focused only on the part which you have mentioned in your question though the matter of sleep as a symbol is connected with Lady Macbeth too.
Sleep does not signify just innocence in Macbeth, it also means internal and external peace.
In Macbeth, Macbeth's utterance: "Macbeth does murder sleep..." is a paradoxical statement. Here, if carefully noted, one can comprehend a deeper meaning of the murder of 'sleep'. This killing is not only the murder of innocence, it is also a sort of alarm or sign which indicates the audience about some ominous thing going to happen in future. Through murdering sleep, Macbeth is not only endangering the harmony of his country, but also his own sleep is going to be vanished soon. In the later parts of the play, we find it to come to be true, since Macbeth becomes a recklessly ambitious person whose sole aim becomes to hold on the royal throne. His greed makes him sleepless or in another sense restless.
In fact, the peace of the country and the nature seems to evaporate just after Macbeth's ascending to the throne. This is evident especially in the conversation between Ross and the old man in act 2, scene 4.