The author likes to call the Akathist Hymn the Annunciation Hymn. I prefer Akathist. Don't mind me. :D
The Akathist Hymn is arranged as a series of greetings to Mary, and it begins with the Annunciation (hence the author's preference). The congregational refrain between oikoi is difficult to translate. It's modeled on Gabriel's words in Scripture, "Rejoice [Xaire], favored one [xarito'o]."
Romanos used "Xaire", but varied the term by which Mary is addressed. Now it is "Xaire, nymphe anymphouete." You can get the general idea by noting that 'nymphe' means bride and that it's followed by 'anymph'. The 'a' prefix usually indicates an opposite. But what's the opposite of bride?
"The paradox the phrase wishes to convey is that, in the conception and birth of Jesus, Mary is genuinely a bride, and yet she remains a virgin."
Translators have tried a lot of variations for the phrase. 'Unwedded Bride', 'Bride without a bridegroom', 'Spouse Unespoused' and 'Bride ever-virgin'. The author has chosen to use 'Unmarried Bride', but points out that it isn't any more accurate than any other translation of the phrase.