The slave cylinder is the workhorse of your vehicle's hydraulic clutch system. When you press the clutch pedal, the master cylinder sends hydraulic fluid down a line to the slave cylinder. The slave cylinder then uses that pressure to move a pushrod, which acts on the clutch fork to disengage the clutch, allowing you to change gears.
If you suspect your slave cylinder is failing, look for these signs: tranny, slave cylinder problems - Truckers Report
Depending on your vehicle's make and year (common in older trucks and Jeeps like the YJ Wrangler), you may have one of two setups: