The device consists of a gear with a ratchet, that vibrates under Brownian motion (hence the name) in a heat bath. The idea is that motion in one direction is allowed by the ratchet, and motion in the opposite direction is prevented. Thus, it might be reasoned, the gear will rotate with a small force continuously in one direction, without any heat gradient. This is against the principle of the second law of thermodynamics, which can be stated as "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work."
Although the Brownian ratchet seems, at first sight, to extract useful work from Brownian motion, Feynman demonstrated through a number of detailed arguments that its operation would be self-defeating, and would in fact not produce any work.
However, this idea led to the development of Brownian motors, which do produce useful work, but do not violate the laws of thermodynamics.