What does the line "Duncan is in his grave; After life's fitful fever he sleeps well" mean?

Macbeth says this to Lady Macbeth in act 3. Both of them are unhappy and tormented by what they have done to get the throne, but at this point, they are both trying to shake it off.
Macbeth, in the line above, is comparing Duncan's state (as a dead man) to his own. Duncan, he says, sleeps well, now that he is dead. He no longer has to be in a "fever" of anxiety about all of life's problems and worries, tossing and turning in his bed at night. Death, Macbeth implies, brings peace: Duncan is not thinking about domestic and foreign threats or the possibility of treason.
In contrast, Macbeth tells his wife that he is tired of being tormented by "terrible dreams" every night. He says defiantly that he won't eat and sleep in fear. He says that it would be better to be dead that to continue to be tormented:

Better be with the dead,
Whom we, to gain our peace, have sent to peace,
Than on the torture of the mind to lie
In restless ecstasy.


His "solution" will be to have Banquo killed.

Macbeth is comparing life to a long, chronic illness, and he imagines death as a peaceful reprieve to this illness. The words "fitful fever" specifically conjure up an image of the turbulence and the disorientation that fevers can bring. This metaphor flips the narrative of death as disease and decay and life as health and happiness. In Macbeth's metaphor, life is illness and pain, and death is sweet release from that pain. This particular line can bring a strange sense of comfort for those who experience tremendous pain in life and are too often told to be positive, or joyous, simply for being alive. This line underscores the sense of tragedy and despair throughout the play. The lives of those in constant tragedy are akin to a life of constant sickness and decay.

Macbeth is using a metaphor to compare life to a sickness in which the patient suffers a fitful fever and death to a cure of that sickness after the patient has passed through a crisis. This is a marvelous metaphor because it is so paradoxical. We think of life as a healthy condition and death as a misfortune. Macbeth is full of beautiful and strange metaphors and similes, which in itself is paradoxical because it is such a morbid tragedy.
The alliteration of F sounds in "After life's fitful fever" should be noted. They are followed by "he sleeps well," which seems especially tranquil after all the F sounds preceding it. They are in "After," "life's," "fitful" (two F's), and "fever." The word "fever" will seem to contain two F sounds because the "v" in fever will sound very much like an "F." So there will be six F sounds in quick succession, since there are two "F's" in "fitful." Is this important? Yes, but only because of its effect on the audience; it makes them glimpse life—their own others'—as nothing but a sort of mad frenzy, a "tale told by an idiot," as Macbeth will decide later on.