Thumbrest is a term associated with handgun grips. Usually it refers to revolvers, but some automatic pistols also have grips that include a thumbrest. Typically, a thumbrest is a carved or molded ledge of material in the top left side of the grip (for a right-handed shooter). When a shooter acquires a grip on his or her gun, the thumb rests on this ledge in a comfortably natural manner.
When bullseye shooting was the main handgun shooting sport, many shooters used revolvers and cocked them in the single action style. It was handy to have that thumbrest just slightly below and to the left of the hammer spur. At that point in history, several craftsmen built special thumbrest grips to the shooter's individual specifications—Roper, Sanderson, Hurst and others. Today, made-to-measure grips are still around, but they are more commonly found on hunting or combat guns.
The thumbrest can be an aid to good shooting, but I personally believe that its greatest value is simply the fact that it helps to establish a consistent grip. Some of them, like the ones still made by Herrett's, are so good that you almost cannot handle the pistol without getting your hand in a proper position. Now, they are original equipment only on a few Smith & Wesson and High Standard rimfire target autos. There was a time when they were often seen in the best of places.