In this context, "Air" is the English term for aria , meaning a lyrical, song-like movement rather than a dance.
Bach composed it around 1730 for a small ensemble of strings and continuo. Air - Johann Sebastian Bach
The piece's haunting beauty has allowed it to transcend the concert hall: Bach’s Air on the G String (Suite no. 3 in D, BWV 1068) In this context, "Air" is the English term