However, the song here is not sung by the husband/husband-to-be, but by the mother and the family of the bride, who are happy that their little girl is a bride on the day and so the words 'my new bride'.
As per a tweet by Swanand Kirkire, Navrai is a bride who loves the moon. Majha is marathi for mine. Majhi, of course, is the female gender for the word.
For the complete translation of the song, SEE THIS POST.