The clutch disengaging, allows for the RPM to increase which then in turn reengages the clutch. The clutch keeps the engine as close to the torque peak of the engine as possible. While this does waste heat, it is very useful when covering a wide range of speeds.
The most common centrifugal clutches have friction pads (shoes) which connect to the inside of the housing. The clutch shoe connects to a various amount of extension springs on the center shaft. When the center shaft turns, the springs stretch out, causing the friction pads to engage the friction face.
There is another type of clutch commonly used in racing karts. This type of clutch has friction and clutch disks stacked on top of each other. A motorcycle clutch also has friction and clutch disks arranged in this manner. The disks are forced together by weighted arms, causing the clutch to engage.
The different arrangements of centrifugal clutches allow for a wide variety of different uses and applications.
"To understand how a clutch works, it helps to know a little bit about friction, which is a measure of how hard it is to slide one object over another. Friction is caused by the peaks and valleys that are part of every surface - even very smooth surfaces still have microscopic peaks and valleys."
- How Stuff Works