Drivetrains work by spinning; crankshafts spin, transmission input shafts spin and so do driveshafts, axles and wheels. Ideally, they should all spin together and in perfect synchronization, but misalignment between the crankshaft and clutch plate will cause some parts to spin on one axis, while other parts continue to spin on another. The symptoms are distinct, but the problem itself is easy to mistake with other issues.
If you've ever taken a back massager apart -- and who hasn't, really? -- then you've seen how it basically works. A massager gets its bounciness from a weight attached to a short arm, which is attached at its other end to the electric motor's shaft. A misaligned clutch plate will do the same thing in your transmission, but in this case, the "weight" is the clutch disc and the "arm" is the distance between the center of the disc and that of the flywheel. Though in this case, the clutch is usually tilted, as opposed to being lifted off of its axis parallel to the flywheel.
"Clutch chatter" is what happens when the clutch rapidly bounces on and off the flywheel, repeatedly grabbing and releasing it -- this is one of the tell-tale signs of a misaligned or damaged clutch mechanism or bearing. In the "damaged clutch mechanism" category, you also have things like oil or water in the clutch material, degraded friction material, a warped or damaged flywheel. this effect becomes even more pronounced over time, as the chattering clutch damages the pressure plate springs and weakens proper engagement.
The clutch may bounce quite a bit before it does finally catch, but when it does, it'll do so with a vengeance. Normally, your pressure plate springs would push the clutch against the flywheel; but when the clutch is misaligned or cocked at an angle, it'll fail to engage until the levering force of its off-axis engagement wedges the plate against the flywheel. When that happens, the clutch will latch onto the flywheel and rapidly grab it instead of smoothly engaging it.
Excess play in the clutch mechanism, combined with the wedging effect, makes the clutch difficult to release and modulate. Ultimately, you wind up with a clutch that works like an on/off switch and chatters during engagement. Misaligned clutch plates are death for the clutch pressure plate springs, the throwout bearing and often the transmission -- so, if you suspect that a problem is brewing, get it dealt with before a $500 problem turns into a $5,000 problem.
