Though I have known about Haydn and his music since I was teenager, I only began listening to his compositions intensively in the past two or three years (after the composer's connection to the area which I now call home solidified in my mind). Despite this, I hadn't encountered the Farewell Symphony at all until Dr. Charlton brought it to my attention. The piece is not only musically wonderful, but it also contains the kind of humorous creative ingenuity Haydn displayed in some of his other works, most notably Symphony 95 - The Surprise Symphony.
Anyway, Haydn and his musicians often accompanied Nicholas, Prince Esterhazy to the fabulous 126 room palace complete with an adjoining opera house the prince had constructed in Eszterháza, a small settlement in rural Hungary approximately 50 kilometers from the Esterházy's main residence in Kismárton (today, Eisentstadt, Austria). The musicians' wives and families were left in Eisenstadt during these stays, which tended to last from approximately May to October.
Nevertheless, in November 1772, Nicholas decided to alter his annual routine and extend his stay at Esterháza for an additional two months. The time extension applied to Haydn and the musicians as well. The musicians, who were all quite homesick at that point and longed to return to their wives and families, beseeched the Kapellmeister to protest on their behalf. Haydn was in sympathy with his musicians plight, but he was reluctant to confront his patron about the matter directly. As a result, he devised a brilliant means through which to bring his musicians plight to Nicholas's attention.
He composed a symphony that included a distinct message. As the piece draws to a close, the players blow out the candles on their music racks and leave the room one by one until only two remain; when the symphony was first performed, the two remaining players were concertmaster Luigi Tomasini and Haydn himself.
Prince Esterhazy took the hint. After the performance, he strode into the antechamber and informed the musicians that he would return his court to Kismárton the very next morning. This is how the symphony became known as the Farewell Symphony.
Dr. Charlton was kind enough to link an excellent performance of this symphony; a performance I highly recommend (the 'farewell fun starts at 21:20 of the video).