The term Dixie, used to refer to the American South, is of unknown etymology. There are several competing theories, but before examining them, let's look at what we do know about the word.
All sources agree that earliest recorded use of the term is the song Johnny Roach, written by Daniel D. Emmett, a blackface minstrel originally from Ohio. The song was first performed in February 1859. Emmett also wrote the more famous Dixie's Land which immortalized the term, and first performed that song in April of that year. While there is no recorded use of the term prior to Emmett's songs, there are attestations that the term was in use before 1859. Emmett himself never claimed to have originated the word, saying that it was one he had heard in use. (Random House Historical Dictionary of American Slang)
So if Emmett did not coin the term, where did it come from? There are three major hypotheses:
The term is simply a reference to the Mason-Dixon Line, the border between Pennsylvania and Maryland that separated the slave states from the free states. Most authorities tend to favor this origin because it is the simplest and most obvious.
The term comes from the French dix meaning ten. The Citizen's Bank of Louisiana issued bilingual, ten-dollar bank notes which bore that French word. These notes circulated widely in the South before the Civil War. The problem with this hypothesis is that no reference to dixies meaning the plural of the bank note has been found.
The term is a reference to Johan Dixie (or Dixy), a Manhattan slave owner of the late-eighteenth and early-nineteenth centuries. Dixie was kind to his slaves, but they were sold South either when Dixie died or when New York abolished slavery. Dixie's former slaves spread stories about how good life was in "Dixie's Land" up north. While it is deliciously ironic to think that Dixie first referred to New York City, there is no evidence to indicate that this is the origin. In 1872, New York Weekly's 30 December issue claimed that Dixie originated in New York City and was associated with a children's game of tag (HDAS). What that magazine's basis for the claim was is unknown.
To summarize, the best guess is that it comes from the Mason-Dixon Line, although no one knows for sure.