The clutch is a component between the engine and transmission which allows the engine's rotational power (via the flywheel) to disconnect from the transmission so the gear ratios within the transmission may be adjusted (otherwise known as shifting gears). It is made out of plates which use friction to connect and transfer the engine's power to the transmission, and when the clutch is applied, these clutch plates are spread apart and no longer transfer that energy.
Most standard cars have clutches with a single plate, but performance cars have up to three to handle more power and shift more quickly. Only manual transmissions have clutches; automatic transmissions use a torque converter instead.