It's not only dry clutches that rattle, all clutches rattle. It' s just that most modern motorcycles run 'wet' clutches and the oil cancels out some of the noise. The rattle comes from the clutch plates bouncing against one another.
Inside a clutch is a stack of metal plates which act like bells as they vibrate. When the clutch is engaged they are pushed against each other, but when the clutch is disengaged they are designed to become unstable. Each clutch plate has a small metal nick in the outside edge so that when the clutch is pulled in the plates are destabilized, helping them separate and disengage the clutch. As the clutch wears the noise gets louder due to the plates gaining more gap between them to rattle into, increasing the noise level.
Aluminum clutch baskets are actually quieter than steel ones due to the softer metal damping the noise. The more teeth on a clutch plate the quieter the clutch will be, again down to reduced plate vibration and movement.