"Edge" begins with a simple yet cryptic statement: "The woman is perfected." The next two lines add a little more context: the woman is "dead," and "smil[ing]" as if her death is an "accomplishment." The poem seems to be equating perfection with death, at least in her case. But why? And who or what has "perfected" her—that is, killed her?
Her "smile of accomplishment" hints that she was responsible for her own death: in other words, she died by suicide. (Because "Edge" was the last poem Sylvia Plath wrote before her own suicide, this is the most common interpretation of the line. The woman is often assumed to be a reflection of the poet, although not all critics agree, since she is also a dramatic character, complete with "toga.")
She seems relieved or fulfilled now that she has "accomplish[ed]" death, which she may have seen as a way of "perfect[ing]" herself. It's unclear, however, whether the equation of death and perfection is hers, the speaker's, or both. The line might be loaded with grim irony; for example, it might be critiquing a world that holds women to impossible standards, and so drives some women to eliminate their supposed flaws by destroying themselves. (The poem has often received this kind of feminist reading.)
"Edge" is written in free verse, but this opening couplet contains a light rhyme on "perfected" and "dead," reinforcing the supposed link between death and perfection. The stark enjambment after "dead" not only creates this rhyme but places extra emphasis on the word, as if to stress the finality of death.