An automotive clutch is a drivetrain component found 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 allow that energy to be transferred.
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, and constant velocity transmissions don't need either.
The clutch is mounted on a splined shaft at the transmission, and to the flywheel.
A high performance clutch is any clutch which is designed to deal with more stress than the original equipment was designed for. This stress may come in the form of more torque, longer lifespan, or heavy driver demands.
Performance clutches need to be able to handle high torque loads from high performance engines. Upgrades usually start with the friction material on the plate, but when that isn't enough performance, the number of plates are increased so the clutch can be smaller, reducing rotational inertia and overall weight.
The picture above is of a high performance, single-plate clutch with copper ceramic friction material. The friction plate is on the left, the throwout bearing is in the top center, and the casing is on the right, in red.