The poem begins by announcing that "this," meaning the poem itself, is a "letter" addressed to the "World." This "World" could refer to the whole of human society, and as such this opening line reveals that the speaker is somehow separate from that society. The capitalization of "World" also underscores its personification: the speaker views the World having the ability to write back, though it has never done so.
Already there's a sense of frustration and/or regret at the fact that the speaker is so isolated, and that the rest of the "World" has failed to acknowledge the speaker's existence. Nevertheless, the speaker wants to pass along some sort of message to this World that he or she has received from "Nature" (which is similarly personified).
These lines are both spare and dense; they use simple words that are at once rich with meaning and intensely ambiguous, raising as many questions as they do answers. Indeed, it's not yet clear what exactly this "News" actually is, but it's possible to interpret it as being a reference to poetry itself.
First off, note that this very "letter" that the speaker has written is, quite literally, a poem. This suggests that poetry is a form of communication, which makes sense: poems are ways for poets to express certain ideas, beliefs, or emotions to other people—they are a means of translating thoughts and feelings into words that other people can read and understand.
Yet this particular poem does not seem to be about the speaker's personal thoughts, but rather about some sort of "News" from "Nature." The speaker implies that poetry's task is to pass on some broader, objective message: taking nature's "simple News" and translating it, as best it can, into terms the "World" will understand. The alliteration of the /n/ sound in "Nature" and "News" underscores this connection: if this "News" is akin to poetry, then poetry itself is something plucked from the natural world. Poetry contains within in it grand natural truths, and it is the poet's job to write this "News" down.
The poem's form is appropriate for its moral and philosophical seriousness. It is written as a ballad, with alternating lines of iambic tetrameter and iambic trimeter, rhymed ABCB. This meter and rhyme scheme was often used for hymns—the religious songs sung in English Church. For Dickinson’s first readers, pious New Englanders who spent a lot of time in Church, the poem’s relationship to the hymn would’ve been obvious.
Dickinson appropriates the majesty of religious music, but not its rigidity: Dickinson’s meter is consistently inconsistent, diverging widely from the expected rhythms of an iambic line. For example, the poem’s very first line contains a spondee (two stresses) in its first foot:
This is my letter to the World
This emphasizes off the bat that this very document is something important and bold, a statement of intent.