The "julep" is an old name for a drink flavored with herbs, and the word was commonly used to describe the mixtures used to deliver medicines. The mint julep became popular in the American South because it was made with domestically produced bourbon whiskey rather than the rum popular in the North, which was made from imported molasses. It was originally drunk partly for medicinal purposes, as mint was used to treat various ailments, and the crushed ice made it a pleasant drink for a hot day. No one is sure exactly where the mint julep originated; About.com's Kathy Hamlin says Georgia is most likely but Virginia is also possible. William Howard Russell, an Englishman visiting a plantation near New Orleans during the Civil War, records being offered one as soon as he woke up in the morning, which he records as being considered "a panacea for all the evils of the climate."

However, the Confederacy's loss of the Civil War and the temperance movement of the late 1800s really hurt the mint julep's popularity. They are drunk now most often as a deliberate imitation of the Old South, such as at the Kentucky Derby. But the mint julep is probably the first truly popular cocktail, long before the heyday of cocktail invention, the 1920s.

Sources:
Barr, Andrew. Drink: A Social History of America. New York: Carroll & Graf Publishers, Inc., 1999.
http://cocktails.about.com/library/weekly/aa042200a.htm