A tourbillon is a mechanism that constantly rotates the balance wheel, balance spring and escapement while the movement is running. This is done to counter the affect of Earth's gravity on the isochronal properties of the balance wheel and spring.
The tourbillon was invented by Breguet in 1795 and patented in 1801. It is a French word that means whirlwind, which aptly describes it's motion. It is mesmerizing to watch the balance wheel oscillate at the same time it is turning 360 degrees. Breguet sought to eliminate positional error, that is the error introduced by keeping the watch in one position for an extended amount of time. His theory was that if the regulating organ of the watch was constantly in motion, the positional errors would be averaged out.
Today, the usefulness of a tourbillon is controversial, as a wrist watch is constantly being moved in different positions as it is worn. The tourbillon is often used as a display of watchmaking virtuosity, commanding high prices.