A clutch slave cylinder is a small tube that the clutch pedal pushes on to release pressure on the clutch. A typical slave cylinder is located under either one of two pedals, or between them. The closer it is to the foot pedal for releasing pressure on the clutch, it's considered "servicing" the brakes or gas and also releases pressure from them.
Usually slave cylinders are made out of steel and contain a rubber vacuum hose running through them which runs from a hole in one end to a nipple in another end, with an airtight seal between the two ends. When the clutch pedal is pushed down, this cylinder releases a small amount of vacuum to allow the transmission to shift into gear.
Under most circumstances, the slave cylinder operates in two ways, either by absorbing mechanical pressure or by releasing vacuum depending on whether the clutch pedal is released or not. When it is released, its function is to release pressure from the brakes and gas pedals.
Sometimes, a car may have more than one clutch slave cylinder. One will be attached directly to one of these pedals and be used primarily for releasing pressure from that brake or gas pedal. It will also be used as a backup in case the primary slave cylinder should fail during normal use.