Eddy Currents and Magnetic Damping
Eddy Currents
These currents are called Eddy currents (like eddy currents in a river or stream). These little eddy currents produce their own magnetic fields that oppose the changing flux. And these induced magnetic fields produce strong drag forces on the falling disk. This process is called magnetic damping or magnetic braking and it used all over the place. One example I can think of is roller coasters.
And here is a slightly less exciting video showing how magnetic braking works in a desktop demonstration:
Physics Education Research at UNG 