The poem kicks off with a mysterious speaker who asks a listener whether they'll "give" themselves over to the speaker "utterly" (that is, absolutely). Based on the poem's title, readers can assume that the speaker is a personified version of sleep. That is, the poem is trying to describe the act of falling asleep by treating sleep itself like a figure that's alluring, seductive, nurturing, parental, and overbearing all at once.
Sleep doesn't just want this person to hand over their body. Sleep says the sleeper should surrender both their "body and no-body," their "flesh and no-flesh." The implication is that sleep dissolves the barrier between one's body and mind.
The poet could have chosen to write this line a little differently—"body and soul, flesh and spirit," for example. But the choice to repeat the word "no" adds some rhythm to the line, as does the asyndeton (or lack of conjunction) between these parallel phrases (and throughout the poem's first four lines, for that matter). The language moves smoothly forward, evoking the pull of sleep.
Sleep goes on to say that this surrender shouldn't be like a fugitive running away from something "blindly and bitterly," with alliteration adding emphasis to sleep's point. Instead, sleep says, the sleeper should give themselves up to sleep "as a child might, with no other wish."
By using a simile to compare the sleeper to a child, the poem casts sleep as a kind of parental figure taking the sleeper into its arms. There is something soothing in this comparison, although there is also a hint of something a little more ominous, as sleep demands complete, unquestioning trust from the sleeper.
The first stanza then concludes with a second voice—the voice of the person sleep is addressing—answering that they will indeed surrender themselves to sleep. They respond using the same language that sleep used: they will trust themselves to sleep's care "utterly." The repetition of the word "utterly" cements the absolute control that sleep will have over the sleeper; the sleeper becomes entirely passive in sleep's care.