"My Life Closed Twice Before Its Close" is a short but ambiguous and rather cryptic poem. The first line, "My life closed twice before its close," seems somewhat paradoxical. The speaker seems to be looking back retrospectively and reflecting upon two metaphorical deaths which preceded her final, literal death. Emily Dickinson uses this retrospective afterlife perspective in other poems, including "Because I Could Not Stop for Death."
The two metaphorical deaths could refer to two incidents of heartbreak, or parting endured by the speaker, which were so severe as to seemingly "close" her life. At the end of the first stanza, the speaker wonders if "Immortality," or, in other words, the afterlife from which she speaks, will bring her a third such "event," or heartbreak.
In the second stanza, the speaker suggests that she won't be able to endure a third such heartbreak. She finds it "hopeless to conceive," meaning perhaps that she can't imagine enduring such pain again, or that she can't imagine surviving such a pain for the third time. The second stanza concludes just as the first began—with a seemingly paradoxical phrase. The speaker says that "Parting is all we know of heaven," implying perhaps that there is a glimpse of something heavenly in the experience of heartbreak. Perhaps she means that when we are parted from someone we love, we experience an intensified form of that love, which is so pure as to be heavenly. However, the poem then concludes with the declaration that "Parting is . . . all we need of hell." The implication here is that although the intensified love is, in its own way, heavenly, it is nonetheless hellish to realize that one must be parted from that love. It is as if the speaker feels hell all the more intensely because she has, albeit briefly, experienced heaven.