This first line introduces the conceit that will guide the poem as the speaker compares his or her state of mind to a funeral. This initial comparison allows readers to draw a host of inferences about what's going on with the speaker. First off, funerals, especially in Western culture, represent a time of sadness, bleakness, and even despair. People mourn by wearing black and expressing a somber attitude. The Puritan tradition—the religious culture at the root of the history of New England, where Dickinson grew up—emphasized piety and moral seriousness over gaiety. Already, then, the poem takes on a rather somber and perhaps mysterious tone.
Right off the bat, the speaker has placed the poem in the past tense ("felt"). Whatever's going to happen in the poem has already happened; the speaker's on the other side of it. Notice, too, how it's left totally unclear who exactly this funeral is for. This creates an air of mystery in the events that follow. The odd capitalization of this line will also recur throughout the poem, suggesting that this is meant to be taken figuratively—that is, that each of these capitalized nouns are being used as broad, symbolic stand-ins for the poem's thematic ideas about death, sense, and reason. The quick caesura also creates a halting, almost uncertain rhythm; already the speaker must pause to clarify his or her thoughts.
Finally, this funeral takes place in the "Brain." Rather than taking place in the abstract region of, say, the "mind," the poem locates itself directly in the speaker's body. This line, then, prepares readers to accept that the metaphorical, emotional, and even mystical events of the poem will all in some way relate to the speaker's own physical self. Here, readers can almost picture a tiny funeral service happening inside the speaker's skull. This isn't to that the metaphor should be taken literally, but that this possibility prepares readers for future gray areas when they might lose track of the metaphor's vehicle and tenor—in other words, for when the poem's extended metaphor becomes more complex, harder to map onto the poem's lines themselves as the speaker's reason begins to break down.