From www.mutopiaproject.org

"Air on the G String", also known as "Air for G String" and "Celebrated Air", is August Wilhelmj's 1871 arrangement of the second movement of Johann Sebastian Bach's Orchestral Suite No. 3 in D major, BWV 1068.
The above text from the Wikipedia article "Air on the G String" text is available under CC BY-SA 3.0.

The four orchestral suites, BWV 1066–1069 are four suites by Johann Sebastian Bach. The name ouverture refers only in part to the opening movement in the style of the French overture, in which a majestic opening section in relatively slow dotted-note rhythm in duple meter is followed by a fast fugal section, then rounded off with a short recapitulation of the opening music. More broadly, the term was used in Baroque Germany for a suite of dance-pieces in French Baroque style preceded by such an ouverture. This genre was extremely popular in Germany during Bach's day, and he showed far less interest in it than was usual: Robin Stowell writes that "Telemann's 135 surviving examples [represent] only a fraction of those he is known to have written"; Christoph Graupner left 85; and Johann Friedrich Fasch left almost 100. Bach did write several other ouverture (suites) for solo instruments, notably the Cello Suite no. 5, BWV 1011, which also exists in the autograph Lute Suite in G minor, BWV 995, the Keyboard Partita no. 4 in D, BWV 828, and the Overture in the French style, BWV 831 for keyboard. The two keyboard works are among the few Bach published, and he prepared the lute suite for a "Monsieur Schouster," presumably for a fee, so all three may attest to the form's popularity.
The above text from the Wikipedia article "Orchestral suites (Bach)" text is available under CC BY-SA 3.0.