This poem is describes what goes on in a house in which someone has recently died. The tone is matter of fact, much like a reporter would notice details. Without mentioning death, she describes all the things that go on after a death: she mentions the "numbness" of the house, but that is the appearance of those who come and go rather than that of the building; neighbors "rustle" in and out, perhaps offering support; the doctor has done all he can, so he leaves; they throw out the mattress of the deceased (giving the boys something to speculate on); the minister comes "stiffly"; then the miller and the man of the "appalling trade" come to prepare the body for burial; and finally the tassels and coaches will come to finish the task.
All of the images and information suggest the formal ways we deal with death; it's a part of life and we have a rituals to put some of the sadness of the event off. Death is the last part of life, and we need to deal with it as such.
This poem reminds me of another poem that is very much like it:
The bustle in a house
The morning after death
Is solemnest of industries
Enacted upon earth, -
The sweeping up the heart,
And putting love away
We shall not want to use again
Again, death is spoken of in terms of "bustle" --- the things we do to put something between us and the experience of death. But this one is, on the surface at least, is more hopeful. Although our hearts as "broken," we sweep them up and put them away, because we shall want to use them/it one day again --- in eternity. It takes the some stale image of the "broken heart" and uses it in a new and interesting way.