The speaker uses the metaphor of death to describe the torment two cataclysmic events inflicted. What these two events are we don't know, and I think there is little to be gained in trying to read the poem biographically; for example, is she referring to the deaths of two people? and if so, to whom? was she in love? were her feelings reciprocated?

What matters is that the pain of these events was so sharp that she feels as if her life ended. Despite her feeling, she is, of course, still physically alive, so that she can experience more than one loss and the pain of that loss. Obviously, "its close" at the end of line 1 refers to her literal death.

Dickinson uses metaphors of vision ("see" and "unveil") for revelation. What happens after death, in immortality? She compares what might be revealed to the pain she suffered twice before.

The last two lines of this poem present a powerful paradox; parting is both heaven and hell. We part with those who die and--hopefully--go to heaven, which is, ironically, an eternal happiness for them; however, we who are left behind suffer the pain (hell) of their deaths (parting). Is there any comfort in this poem? What is the one thing we "know" about heaven? Is heaven, for living human beings, connected to hell? A personal note: these lines chill me every time I read them, and they stay with me afterward.