A clutch is a subcomponent of an engine's transmission designed to allow engagement or disengagement of the engine to the gearbox or whatever apparatus is being driven.
There are many different clutch designs, but most are based on one or more friction discs, pressed tightly together or against a flywheel using springs. The friction material is very similar to the material used in brake shoes and pads and used to contain asbestos. The spring pressure is released when the clutch pedal is depressed and the discs are held less tightly and allowed to rotate freely. A wet clutch is immersed in lubricating fluid to keep the surfaces clean and to cool it, for improved performance and longer life; while a dry clutch is not.
In a car it is operated by the left-most pedal using hydraulics or a cable connection from the pedal to the clutch mechanism. No pressure on the pedal means that the clutch plates are engaged (driving), while depressing the pedal will disengage the clutch plates, allowing the driver to shift gears.
On most motorcycles, the clutch is operated by the clutch lever, located on the left handlebar. No pressure on the lever means that the clutch plates are engaged (driving), while pulling the lever back towards the rider will disengage the clutch plates, allowing the rider to shift. Some mopeds have an automatic clutch, using centrifugal forces to engage the clutch above certain rpm.
When engaging the clutch, the engine speed may need to be increased from idle, using the manual throttle (UK: accelerator), so that the engine does not stall. However, raising the engine speed too high will cause excessive clutch plate wear and cause a harsh, jerky start. This kind of start is desired in drag racing and other competition, however.
A clutch may also be a device on a shaft that will "slip" when higher than normal resistance is encountered on a machine. A example of a clutch such as this may be mounted on the driving shaft of a large grass mower. The clutch will "slip" or "give" if the blades were to hit a rock, stump, or other immobile object.