In the first lines of this poem, the speaker makes the "bold" decision to take a simile quite literally. When the wind taps on the door "like a tired Man"—an everyday noise evoked by those alliterative /t/ sounds in "tapped" and "tired"—the speaker doesn't just ignore it, but makes "like a Host" and invites it in.
Listen to how this personified wind comes in the door:
[...] entered then
My Residence within
At a first glance, these lines might seem redundant: if the wind "enters" the house, of course it's "within." Read another way, though, these words suggest that the wind is entering the speaker's "Residence within" in a more intimate sense. Entering the house and then going "within," the wind might also be entering the speaker's internal residence, the speaker's inner world.
This will be a poem about what it means to invite such strange visitations. To this speaker, the most ordinary wind at the door can be an object of fascination, a guest well worth hosting. What's more, paying this kind of attention to the natural world can also mean inviting something new "within"—that is, being inspired. "Inspiration," remember, is airy: at its roots, the word means "breathing in."
Dickinson will smuggle this poem's wild vision in the plain brown paper wrapping of ballad stanzas: quatrains rhymed ABCB, written in alternating lines of iambic tetrameter (lines of four iambs, metrical feet with a da-DUM rhythm) and iambic trimeter (lines of three iambs). Here's how that meter, also known as common measure, sounds in the poem's first two lines:
The Wind | – tapped like | a ti- | red Man –
And like | a Host – | "Come in"
Common measure is called common measure because it's, well, common. This solid, familiar old form will contain the poem's mysteries just as the speaker's ordinary house contains its strange visitor.