• (n.) The night in which a person is born; the anniversary of that night in succeeding years.
Birth'night` noun The night in which a person is born; the anniversary of that night in succeeding years. « The angelic song in Bethlehem field, On thy birthnight , that sung thee Savior born. Milton. » 
the night of a person's birth, esp. a birthday celebration for royalty. · the anniversary of such a date. · the celebration of a royal birthday.