This sure is a sleepy poem, isn't it? Yes, sleep is everywhere—both sleep as in sleeping and in Sleep, the personified, imaginary being who grants slumber. Come to think of it, in some ways, sleep is the speaker's occasion for metaphor practice; the first four lines contain six metaphors which attempt to explain just what sleep does. If sleep is the great healer, however, it is also a door to an imaginary or idealized world. The real reason the speaker wants to sleep is so he can see the dream version of his beloved, Stella. Even though this isn't really totally obvious in this poem (check out "Sonnet 38" for that), it's important to know that the speaker's eagerness for sleep stems in part from this desire to "see" Stella.
Lines 1-2: The poem opens with the speaker addressing and apostrophizing a personified Sleep. He then goes on to describe Sleep with three different metaphors ("knot of peace," "bating place of wit," "balm of woe"). All three make Sleep seem like a healer: a balm for one's sadness, a place of rest and refreshment, a metaphorical glue that maintains peace.
Lines 3-4: The metaphor fiesta continues in these lines as the speaker gives us three more. This time, Sleep is called "The poor man's wealth, the prisoner's release" and "The indifferent judge between high and low." The point of the metaphors is that sleep gives us what we need most (wealth for the poor man, freedom for the prisoner). The metaphor about the judge is the speaker's way of saying that sleep makes no distinction. It is equally available to all, to both the high and the low, rich and poor, prisoners and free men. Note again the alliteration of the P words here ("poor," "prisoner").
Lines 5-6: The speaker asks Sleep to "shield" him from a crowd of "fierce darts" that Despair is throwing at him. The personification and the metaphor (Despair isn't really throwing darts at him, is he?) are conventional, but they also make the speaker's suffering or despair seem more vivid, more violent, and more troublesome.
Line 7: The speaker issues another plea and asks Sleep (yes, he's still personified) to make the "civil wars" inside him "cease." "Civil wars" is a metaphor for some emotional conflict inside the speaker, perhaps between despair and hope, reason and irrationality. It's anybody's guess really. Sleep, as we know from line 1, is (metaphorically) the "knot of peace," so it can bring these battles to an end.
Lines 9-11: The speaker offers Sleep a whole bunch of sleepy things: pillows, a bed, and a "chamber deaf to noise and blind to light." Sleep, in addition to everything else the speaker tells us he is, is now made into a being that can "take" things. This personification makes him seem more and more alive.
Line 12-14: The speaker continues to develop an image of Sleep. Here he is presented as a being that can be moved, and is apparently hard to move. Well darn. The whole bit about seeing Stella's image inside the speaker is a bit strange, but we see this as a metaphor for how the speaker's feelings and relationship: he loves her and thinks about her all the time. Her image is "inside" him.