The tune for The Star-Spangled Banner comes from a song called To Anacreon in Heaven. It was written for use by a men's club, called The Anacreontic Society. They met once a month at a place called the Crown and Anchor Tavern. The Crown and Anchor was not just a tavern in the sense we think of today, but had a dining hall suitable for performance by a small orchestra. Some of the best known entertainers of the day performed there.
The Anacreontic Society was named after the classical Greek poet Anacreon. Although many Roman poets wrote about themes of "wine, women, and song," few Greek poets did. Anacreon was an exception, so his name came to be associated with rather rowdy parties. In the song, the members of the Anacreontic Society "pray" to Anacreon, petitioning him to be their inspiration. Anacreon agrees and offers to teach them to "intwine the myrtle of Venus with Bacchus' vine." In Greek mythology, Venus is the goddess of love and Bacchus is the god of wine. Jove, the God of thunder and king of the gods, objects that this is too fine a gift for mere mortals. He threatens to hang the members of the Anacreontic Society. This parallels the myth of Prometheus, who was punished by Zeus for giving mankind the gift of fire. In the Anacreontic song, however, the other gods rally around the members of the Anacreontic Society and protect them. In the end, Jove (Zeus to the Greeks) is convinced that the Anacreontic Society deserves the approval of the gods and lends his support.
The Anacreontic Society was dissolved in the 1790s, but not before it spawned a host of imitators. In the new United States, cultural ties with Britain continued after independence. Anacreontic Societies were formed in the U.S., which helped to spread the tune. It makes a good tune for patriotic songs, and many such songs were written in the US. Several are printed in this site.
The words and music were written by two different members of the original Anacreontic Society. The words were written by a man named Ralph Tomlinson. The music was probably written by John Stafford Smith, but this is not completely certain. We also do not know exactly when the music was written or whether the words and music were written at the same time. It is interesting that the tune that was to become the national anthem of the United States was probably written by an Englishman not long after the time of the American Revolution. It is also ironic that our very solemn national anthem was written to a tune that was essentially an invitation to party hearty.
The song contains a number of references to Greek mythology. In case you aren't as fluent in Greek mythology as educated people were in the 18th century, I've added some notes in [green]
