Although the complete history of the unicycle is unclear it is believed that it's an early derivation of the penny farthing. Penny farthings had large front wheels, with direct drive hubs, and very small rear wheels. In the late 1800's, penny farthing riders began riding only on the front wheel in Vaudeville style shows. Eventually they dropped the rear wheel and the unicycle was born. As such it predates the modern bicycle. Today unicycling can be broken into five main categories, on top of just basic riding.
An artistic form of unicycling much like figure skating. Performed on flatland it is generally done with 20" wheel, a high seat and light components.
The form of unicycling as transportation. Involves riding untechnical trails, streets, roads, highways and long distances. Touring unicycles usually have large wheelsizes like, 28", 29" and 36". They are often equipped with brakes, handlebars, and more comfortable seats.
Short for Mountain UNIcycling, involves rough terrain, with rocks and roots, often times downhill. Wheelsizes of choice are 24" and 26" but some muni is being done on specially equipped touring unicycles. A brake is sometimes used along with fat tires and strong components.
A form of unicycling where the main objective is to successfully make it over, through or passed, obstacles. Includes things like hops, drops, gaps, and balance lines. Almost exclusively done on 20" wheels with strong parts and soft fat tires.
The newest form of unicycling. It can best be described as skateboarding on a unicycle. A combination of freestyle and trials, its generally done in urban and skatepark environments. Involves doing tricks on flatland as well as over and off of obstacles. 20" unicycles are normally used with soft fat tires and strong components.