The most central device of "I felt a Funeral, in my Brain" is its conceit, which occurs throughout the entire poem. The speaker compares his or her state of mind to a funeral. Right off the bat, this signals an inner sadness in the speaker, a sense of mourning. Additionally, because funerals involve multiple stages, this comparison gives the speaker room to flesh out this conceit as the poem progresses.
Particularly, the poem situates this funeral in the "Brain." This signals that the poem, on one hand, operates in an imaginary space. On the other hand, it locates that space directly within the head of this particular speaker. As the funeral proceedings go on, it's always clear that this is happening inside a particular person.
The stages of the funeral can be thought of as follows:
Stanza 1: The Wake
Stanza 2: The Funeral Service
Stanza 3: The Funeral Procession
Stanzas 3 and 4: The Funeral Toll
Stanza 5: The Burial
If funerals help the dead move on from this world to the next, then the poem's final stanzas accomplish a similar action. The speaker's falling in the last lines becomes a kind of burial. By the end of this burial, the speaker has effectively disappeared from the world.
So, what exactly is this a funeral for? Following the theme of madness, we could say it's the death of reason. With regard to the theme of despair, it's the death of happiness or of a sense of self. Or perhaps it represents obliteration in the face of the universe's unknowability. However you choose to interpret it, some part of the mind has died.
Furthermore, the funeral really depicts two ends. The first, we've already addressed: something has died in the speaker. That has already happened at the start of the poem. The second end is the end of the funeral, the actual putting to rest. This comes in the poem's final stanza, the explicit silencing of the speaker in the unfinished phrase "- then -." If funerals, in part, serve to guide the soul of the deceased into the next world, that's exactly what happens in this poem as well. The speaker's mind gets transported beyond the known world. And that's ultimately what the poem leaves readers with: a kind of transport, albeit an unhopeful one.
The conceit also acts as a transport in another sense: it becomes literal. Throughout the poem, the line between the metaphor's vehicle and tenor (that is, the line between the thing evoked for the sake of comparison, the funeral, and the subject being described, the speaker's state of mind) gets blurred; the metaphor seems to become real. Readers are so inside the speaker's inside, and the details of the funeral get so fleshed-out, that they might start taking the funeral seriously. Readers lose track of what certain aspects of the funeral might represent (who are the mourners? what is the service? what's in the box?). Instead, these elements become mysterious entities with lives of their own.
In the hands of a poet with less control, some readers might see this as messiness. Here, though, the poem achieves such evocative images and insights that this confusion seems worth it. Indeed, instead of confusion we might think of this as a kind of fusion, a wedding of vehicle and tenor that exemplifies the power of language and metaphor to transport readers beyond mundane comparisons into a realm of greater insight.