Sleep, or a lack of sleep, has a prominent place in Macbeth. On their return from battle, Banquo and Macbeth are surprised by the witches. When the witches tell the men of their destiny (for Macbeth to be king and for Banquo to be the father of kings), Macbeth is preoccupied by the claims, whereas Banquo tries to play them down. Banquo prefers to discuss Macbeth's future rather than his own. He is aware of Macbeth's excitement, but he does not trust the witches or their motives. He worries about how "the instruments of darkness tell us truths... to betray us in deepest consequence" (I.iii.125). 

Accordingly, Banquo is unable to sleep. He is very tired but does not want to sleep because the previous night he dreamed of the witches, and he knows that he may do so again. He does not want to be disturbed and troubled by "cursed thoughts" in his sleep (II.i.6). 

Lady Macbeth is somewhat disturbed by the vision of Duncan as he sleeps because he resembles her own father, and it is this that prevents her from killing him; she sends Macbeth to do it instead. Macbeth becomes quite obsessed with sleep, and he believes that "Macbeth does murder sleep" after he kills Duncan (II.ii.36). He knows he has killed an innocent man, and he deserves no rest such as sleep would bring. 

Sleep should represent peacefulness, rest, and rejuvenation. In Macbeth, it signifies the exact opposite.  

In Act II, Scene I of Macbeth, Banquo cannot sleep because strange thoughts come to him when he does. He tells Fleance:

"A heavy summons lies like lead upon me, /And yet I would not sleep./ Merciful powers, /Restrain in me the cursèd thoughts that nature /Gives way to in repose" (lines 6-10). 

In other words, while the "summons," or call to sleep, lies on him as heavy as  lead, he does not want to sleep. He calls on the "merciful powers" to stop the nightmares that visit him in sleep, as he dreams about the weird sisters and their prophecies.

Later in the scene (lines 19-20), he tells Macbeth that he dreamt of the weird sisters the night before, and he wonders if their prophecies will come true, as some of what they have predicted has already come true for Macbeth. The theme of troubled sleep runs throughout the play, as Macbeth has trouble sleeping when he is consumed with guilt after killing Duncan. 

When Banquo sleeps, he dreams about the three witches and their prophecy.  He feels the witches are evil, and is frightened and troubled.