There are a large number of problems that can cause clutch judder (originally a British term). The problem generally happens when your car is at a complete stop and you engage the clutch. The clutch jerks, alternately gripping and slipping when you let the pedal out. Judder is not only an irritation, but a safety hazard as well.
Parts of the Clutch
A clutch is made up of three different parts: (1) The clutch disk is the "sticky" part of the assembly, which transfers the engine's power from the fly wheel to (2) the pressure plate, which connects to the transmission. (3) The release bearing connects to the clutch pedal, and it unites or separates the other two pieces as necessary. Any of these parts can interrupt the chain of power transfer, and cause the clutch to judder.
If the pressure plate gets overheated--perhaps from letting your foot rest on the clutch pedal, constantly causing the contact between the plate and the disk to change--hot spots can form that warp the pressure plate, or the disk can wear unevenly. Once this happens, consistent contact is impossible. Likewise, if the plate gets bent during assembly, or if the flywheel was resurfaced unevenly, it will not apply pressure consistently when it is engaged against the disk. A warped clutch disk can have the same effect; uneven wear patterns will cause slippage. Incorrectly-torqued screws can distort components also.
Anything that gets the "line of transmission" off-centre can cause problems. On the motor side of things, defective motor mounts can allow the motor to angle slightly, or a misaligned flywheel can cause a wobbling effect as it rotates. On the transmission side of the clutch assembly, similar problems could include bad transmission mounts, bent transmission tie bars, bad or misaligned U-joints or a driveshaft installed at too sharp an angle to the transmission.
Sometimes oil or dirt can get on the face of the pressure plate, creating slick spots that grab for a moment before losing traction against the clutch disk. The clutch disk can also get contaminated, as it is generally made from the same materials as your brake pads. Oil and grease can also contaminate rubber mounts. If the rubber softens, it will deform and allow excessive movement and/or misalignment.
While it is not as likely as some of the other causes of clutch judder, you could simply have a part that was defective from the start. A small percentage of defects during manufacture is inevitable, and even the best inspection system will not catch them all. Besides the obvious possibility of a distorted pressure plate or clutch disk, the moving parts of the release bearing should also be checked.