The first three stanzas of the poem all feature apostrophe, as the speaker directly addresses the "voice" of the poem's title. This voice belongs to the "Woman much missed" of line 1—that is, to the speaker's dead lover, someone he (thinks he) hears calling to him.
Apostrophe creates a sense of intimacy throughout the poem, as though the reader is privy to a deeply personal conversation. The use of apostrophe also reflects the speaker's longing to communicate with someone who is no longer around.
Of course, this conversation is one-sided. The speaker says that the woman calls to him, but readers never actually hear her; she's never quoted directly in the poem, and the speaker effectively tells her what to say in the second stanza. As such, it's unclear whether the speaker is really hearing any voice at all or simply letting his imagination run wild.
Indeed, when the speaker asks the voice if it's really his beloved that he's hearing or if it's just the breeze, there's no direct reply (at least not one put on display for the reader to hear). Apostrophe thus emphasizes the divide between life and death, making the poem seem more monologue than dialogue.
Notably, the last stanza drops the apostrophe and refers to the voice as "the woman" (not as "your voice"). This emphasizes that the speaker is, in the end, alone.