The poem begins with the speaker telling the reader "not [to] stand" next to their "grave, and weep." Right away, then, the reader knows that the speaker is someone who has died and been buried but doesn't want their loved ones to mourn at their gravesite.
That's because, the speaker continues, they're "not there" and they "do not sleep." "Sleep" is a euphemism for death here. The speaker is saying that while their body might be in the ground, their true self (their soul, essence, spirit, etc.) is not—and, indeed, is still awake and alive.
The use of anaphora in these opening lines (the repetition of "I") creates a sense of momentum that carries the reader forward. It also makes the speaker's statement sound more insistent and confident.
Note that this poem has been published in various forms throughout its history. We're using the earliest known published version, which includes line breaks after "stand" and "there." Later versions often omit these line breaks, however, which makes sense when readers consider that they sound like two iambic tetrameter couplets when read aloud:
Do not stand by my grave, and weep.
I am not there, I do not sleep—
Iambic tetrameter means the lines consist of four iambs (poetic units with an unstressed-stressed syllable pattern). Right away, though, the poem uses some variations on this meter. The first foot here scans most naturally as a spondee (two stressed beats in a row) and the second as a trochee (the opposite of an iamb, stressed-unstressed). As a result, that opening "Do not stand" sounds much more forceful and emphatic:
Do not | stand by | my grave, | and weep.
I am | not there, | I do | not sleep—
The general iambic rhythm, meanwhile, lends the poem a steady, familiar sound that's appropriate for a poem meant to offer comfort.