In "Because I could not stop for Death—," the speaker describes her own death, and it is a surprisingly civil affair, rather more like being courted by a would-be suitor than being terrifyingly whisked off by a grim reaper. In the lines in the question, which come from the fifth stanza, the speaker describes the "House" to which the personified Death brings her near the end of their lovely and leisurely ride together. They've seen the school and the young children playing there, the crops in the fields, and even the sunset, but now it grows late and cold, and it seems like time to retire, once and for all.

This "House" seems to be the speaker's own grave, as she says that it seems to be a "Swelling of the Ground" and that its "Roof was scarcely visible," likely due to the fact that the "House" is, in fact, buried beneath the ground. Therefore, it is not a literal house at all—a place where someone lives—but, rather, a metaphor, as it will now house her body only.

Further, the only part of the grave that would be visible would be the very top: the grave stone or marker itself. A "Cornice" is a projecting piece that crowns or tops a piece of architecture, like a house, and so this word choice continues the metaphor of the grave as the place that will house the speaker's body, though her soul seems to move on, as she says that she and Death only "pause" before this "House" before making their way "toward Eternity."