In the days of steam locomotives, the gauge that indicated the level of water in the boiler was a float in the reservoir attached by a metal rod to a ball. When the tank was full, and the train could thus safely reach top speed, the conductor could see a high ball. The term highball came to be used for the signal (two short blows of the whistle and then one long) that a train preparing for full-speed-ahead would issue and then simply for any very fast train.
More commonly, a highball is a mixed drink consisting of a base liquor and a mixer -- usually soda or juice but sometimes water, served in a tall (highball) glass. Florida Highballs use orange or grapefruit juice as the mixer -- as in a Tequila Sunrise or a Greyhound, and New England Highballs use cranberry juice -- as in a Sex on the Beach. Standard Highballs (qualifying for neither of the above special categories) include Gin and Tonic, Seven and Seven, and Scotch and Water.
Patrick Gavin Duffy, an early bar-writer, claimed to have brought the highball to America in 1895. It seems a dubious distinction given the (lack of) complexity of the class of drinks, but he may have been the first to categorize mixes this way.