What does the line "sleep that knits up the raveled sleave of care" mean in Macbeth?

Macbeth makes this statement after he returns to his chambers in an emotionally overwrought state, having just murdered Duncan. The line itself means that sleep is a soothing time that heals or sews up all the worries and stresses ("cares") of the day. It makes us new again, just as knitting up an unravelled sleeve makes a sweater new again.

Macbeth tells Lady Macbeth that from now on the "balm" of sleep is over for him. He will no longer be able to rest in peaceful slumber after what he has done. The evil of his treacherous act will haunt him, keeping him up at night. When he says he has "murdered" sleep, he means he has murdered his peace of mind along with murdering his good, "meek" king.

Although Lady Macbeth tells Macbeth to get a grip and wash the blood off his hands, she is the one who, ironically, will be most affected by the guilt that haunts her in her sleep, unable to wash the metaphoric blood off her own hands.

Sleep is a prominent theme in Macbeth, with sleeplessness being strongly associated with guilt and restlessness. Eventually, Lady Macbeth reaches a point at which she cannot prevent her guilt from exhibiting itself in the form of hallucinations and somnambulance when she is sleeping. It was believed in Shakespeare's time that sleep was a restorative, necessary for soothing the body and mind—something that is, indeed, scientifically true. In this line, sleep is described as a method of renewal; the "raveled sleeve" is what, in modern English, we would term unraveled. That is, the line refers to a sweater sleeve that has started to fray and come unknitted because of excessive use ("care") and is in need of "knitting" up again. When we feel frayed and unraveled, it is sleep that has the power to restore us by metaphorically knitting our fibers back together. Without recourse to this restorative, we will remain "raveled" and unsettled, as Macbeth is feeling.

What figure of speech is used in the line, "Sleep that knits up the ravell'd sleeve of care" in Macbeth?

This line from Shakespeare's Macbeth uses personification and metaphor.

Sleep is given human characteristics by the suggestion that it can sew--knit up something.  This is personification.  Sleep possesses healing powers and can put back together what a day's trials tear apart. 

And care is metaphorically compared to an unraveled sleeve. 

In other words, after a rough day when everything seems to be unraveling, sleep sews everything back up.  And Macbeth has murdered sleep--sleep will be no more.   The daily cares of life are the tenor of the metaphor, and sewing up an unraveled sleeve is the vehicle by which the tenor is explained. 

The line contributes to the insomnia prevalent in the play.  

Sleep is being personified here in this quotation from the play "Macbeth" by William Shakespeare. The author is using several images and symbols to show us how people derive therapeutic rest and recuperation from daily stresses through sleep. He is saying that sleep is like a person (a mother?) who knits or darns holes such as those in a sock or garment which has become ragged and frayed through overuse or rough handling. In the same way, the restful therapy of sleep should ease all our cares away, remaking our tired and frazzled souls during the night. Sadly, for MacBeth and Lady MacBeth, the strain of their guilty and evil plans denies this balm of sleep. Guilt and fear keep them awake at night and cause nightmares and sleepwalking.

In addition to the other editors' posts about personification, Macbeth's quote in Act II, scene ii of Macbeth is a metaphor (an analogy), and it is filled with two types of imagery.

Metaphor / Analogy: Translated, it means, "sleep that straightens out the tangled coil of worry."  Macbeth and his wife have murdered Duncan and sleep, so Macbeth is comparing the act of sleep to to the act of unravelling.  Sleep unravels worry the same way a weaver unravels thread.  He will not sleep for the rest of the play; instead, he will forever worry and be paranoid that someone or something supernatural will discover his crime.

Imagery: the line contains two types of imagery: "sleep" and "clothing."  The leitmotif of sleep runs throughout the play.  The lack of sleep is a result of guilt, and it will drive both Macbeth and Lady Macbeth crazy by the end of the play.

Macbeth is also full of clothing imagery: "borrowed robes," the "crown," and "the sleeve."  These images underscore the domestic and gender differences between the couple.  Ironically, Macbeth makes an analogy here about a feminine domestic duty (sewing).

I think that you can argue that there are two figures of speech in this passage.

First, you could argue that there is a personification here.  You can say that the speaker is saying that sleep can knit things, which obviously it cannot.  That's personification -- giving something that is not alive the ability to act like a living thing.

Second, you could say that there is a metaphor.  The speaker is comparing a person's worries and cares to a knitted sleeve that is coming unraveled and has to be mended.  Because the speaker does not say "cares like a sleeve..." it is not a direct comparison.  That means it's not a simile.

Explain Macbeth's speech about sleep and the 'raveled sleeve of care' in Macbeth.

It seems possible that Shakespeare wrote some of his monologues as separate poems when the thoughts occurred to him, then saved them to insert in his plays in convenient places. This could have been true of Hamlet's "To be or not to be," Jacques' "All the world's a stage," and others such as the one about sleep to which your question refers. Shakespeare valued sleep and wrote about it in a number of places. Here is his sonnet XXVII:

Weary with toil, I haste me to my bed,
The dear repose for limbs with travel tired;
But then begins a journey in my head,
To work my mind, when body's work's expired:
For then my thoughts, from far where I abide,
Intend a zealous pilgrimage to thee,
And keep my drooping eyelids open wide,
Looking on darkness which the blind do see
Save that my soul's imaginary sight
Presents thy shadow to my sightless view,
Which, like a jewel hung in ghastly night,
Makes black night beauteous and her old face new.
Lo! thus, by day my limbs, by night my mind,
For thee and for myself no quiet find.

Macbeth wanted to murder King Duncan in order to take his place--but the King had two sons, both of whom were also sleeping under Macbeth's roof on that fatal night. The older son, Malcolm, was the heir apparent. Macbeth should have killed both Malcolm and Donalbain that same night. Shakespeare knew this. But he hoped his audience would accept the way the two sons escaped, making it possible for Malcolm to flee to England and raise an army.

Macbeth returns carrying two daggers, suggesting that he had intended to murder Duncan's two sons but something had forced him to flee to his bed chamber. He tells his wife:

Methought I heard a voice cry 'Sleep no more!
Macbeth does murder sleep', the innocent sleep,
Sleep that knits up the ravell'd sleeve of care,
The death of each day's life, sore labour's bath,
Balm of hurt minds, great nature's second course,
Chief nourisher in life's feast,--

Whether the voice was real or imaginary, Macbeth felt he had to go into hiding or be caught with bloody daggers and bloody hands. A few lines later he says:

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.'
                                                     (II.2)

The voice is crying, or shouting, and threatening to expose him "to all the house." Otherwise, it would appear, he would have stolen into Malcolm's chamber and murdered him in his bed, and then stolen into Donalbain's chamber and done the same thing. The triple crime would, of course, have to be blamed on someone else; but if Macbeth subsequently murdered Duncan's grooms, the perpetrator of the three homicides could remain a mystery. It could have been anybody!

Shakespeare inserted his beautiful lines about the innocent sleep as a distraction to keep his audience from wondering whether he did indeed intend to kill the two sons. The conclusion of his monologue foretells his terrible punishment for murdering the King while the old man was enjoying his innocent sleep. Now Macbeth will have to lie awake every night reliving and regretting his crime, as well as listening fearfully to every sound inside and outside his room. His insomnia will cause him to experience hallucinations and become mentally incompetent to rule the kingdom he usurped. He will commence an orgy of killings, hoping to save himself from assassination by eliminating any probable enemies.