A French cuff (or double cuff, as they're called in England) is a cuff which extends beyond the intended arm length of the shirt or dress it is fitted upon. The idea is to fold the cuff back and use cufflinks to keep the cuff in place.
The history of cuffs on shirts is a somewhat active and highly individualized account, with hundreds of alterations and changes occurring throughout the centuries. The first idea of the modern dress shirt evolved sometime during Victorian England, and these shirts would often employ buttons at the sleeves. While the very rich could afford custom tailor jobs, most people simply bought generic "one size fits all" dress shirts. These shirts' sleeves erred on the long side, with multiple buttons down the side so the wearer could button it at their wrist, and then fold the excess fabric back up the sleeve - thus covering the extra buttons as well.
Sometime in the mid 19th century, the rather snooty French dropped this convention and began manufacturing individually sized shirts. They kept the tradition of the excess sleeve, however, in the form of the French cuff - but dropped the buttons in favor of cuff links.
With the rise of non-white dress shirts in the 20th century, French cuffs have fallen out of favor as cuff links become harder to accessorize succesfully. Still, they are a favorite of board rooms and corporate headquarters everywhere, and nearly 15 million French cuff shirts were sold in America in 2004 alone.