Basically the clutch hydraulic system has two parts. The master cylinder which is worked by the clutch pedal, and the slave cylinder which moves the clutch release fork. They're connected by a hydraulic line.

You press the pedal, the master cylinder moves fluid in the clutch line to the slave cylinder, which moves the release fork. If the slave cylinder is busted the pedal no longer has full control over the release fork because there is no direct linkage.