In watchmaking, mechanism refers to any system of components that transforms energy or controls a specific function within the movement. The distinction that really matters, however, is between basic mechanisms and complication mechanisms: the former serve to measure time, the latter add functions that the train of wheels alone cannot perform.
The most discussed mechanism in chronographs is the column wheel. It's a drum with stellar cams that coordinates the start, stop, and reset of the chronograph with mechanical precision superior to eccentric cam systems. When paired with a vertical clutch, the central hand starts without slippage or micro-bouncing. I've disassembled both systems on my bench: the difference is felt on the wrist, but seen even better under the magnifier. The column wheel costs more working hours, which is why you find it displayed at 6 o'clock on models where the maker wants you to see it.
The jumping hour mechanism is among the most demanding to regulate. It must accumulate energy for hours, then release it all in an instant so the disc or window displays the new number without bounce. One hour fast or slow means an entire readjustment. The retrograde mechanism works similarly: a spring accumulates tension as the hand advances, then releases it abruptly. Urwerk, in the UR-150, replaced the Malta cross with a rack-and-cam controlled by a speed regulator, achieving a zero return in one hundredth of a second.
The tourbillon is a compensation mechanism: the rotating cage carries the escape wheel and balance together to neutralize gravity's effect on the escapement. F.P. Journe's Remontoire d'Égalité works differently, regulating the force transmitted to the balance at constant intervals, so that variations in the mainspring never reach the escapement. Daniels solved the wear problem with the Co-Axial: an escapement with three impulse planes that reduces friction without needing frequent oiling, first tested on a pocket watch, then adopted by Omega in 1999.
There are mechanisms that abandon hands altogether. HYT uses pistons and bellows to move a liquid along a capillary: the mechanical movement remains, but the output is fluid-dynamic. F.P. Journe in the Vagabondage uses rotating discs. These are rare solutions, difficult to repair outside the maison, and this is a technical fact that those who buy them should keep in mind.