I will echo the above. Dickinson's point was about how although we see death as a major event, in the natural world it is not. Death is an every day occurance. Sitting with someone as they die is not enlightening leading to epiphanies--it is quiet and anti-climatic. We want our lives--full of sound and fury--to end with a bang--but often they don't, hence the housefly. This poem puts into perpspective how regardless of the kinds of lives we live, we all end our lives in the same way. The mundane--the fly--and the profound--life after death--can be perhaps one in the same.
This poem is unique in several ways, but perhaps most significantly because it is a narrative of a person's death by that person. So this suggests, in a way, that there is some existence after death. But the person's description of the actual process of dying is mundane and even macabre. The narrator's passage into death is not heralded by visions of a beautiful afterlife (indeed, the fly "interposed itself between the light" and the narrator) or by meeting the Almighty. Meeting "the king" seems to be expected, but not realized. Instead, the buzzing of the fly, which obviously carries an association with morbidity and rotting corpses, is the only sensation the dying person experiences before finally expiring. Ultimately, this poem is an expression of the ambiguities, uncertainties, and ultimately, the fear of death that plague even people of devout religious faith. The fly encapsulates all of these emotions, even though it is a mundane little insect.