What is the purpose of the plastic disk between the cassette and the rear wheel?

From Sheldon Brown:

Spoke Protector

A plastic or sheet-metal disc that fits between the cluster and the right-side spokes of a rear wheel. This is intended to prevent the derailer or chain from getting caught in the spokes, possibly causing very extensive/expensive damage/destruction to the wheel, the derailer, and the frame.

A spoke protector is not a necessity on a bike that is well treated, because the derailer can't go into the spokes if it's properly adjusted and if it is not bent. Bicycles which are subjected to rough handling, however, are prone to getting the rear derailer bashed in, and in such a case, the spoke protector can prevent very serious damage.

And from purely personal anecdotal experience: I have a friend that doesn't like spoke protectors and has been pretty vocal about it. Faith would have it that a maladjusted XTR derailleur wrecked his wheel and destroyed itself. A spoke protector would have prevented just that.