Paper prototyping is essentially a representation of the game on a non-digital medium. Meant to mostly be low-fidelity, quick-and-dirty representations of the game, or particular aspects of the game; paper prototyping is mostly used to test functionality of the core mechanics, new features, UI functionality, or even entire game systems.
Naturally, paper prototypes often require their own set of rules that attempt to aggregate the rules of the game system, and in such an aggregation, there will certainly be some elements lost in the digital to non-digital translation.
Nonetheless, I personally believe in paper prototyping as not only is it quick-and-dirty, it also gives people a good feel of the game in play. Despite being a dummied down or sometimes really slow representation of the actual digital game, there are certain issues that can be identified with the game systems even in the early stages of paper prototyping, and it is best to address to be able to test and address whatever can be tested on paper, before moving on to digital prototyping, which is a whole new can of worms.
Mūzaïc Paper Prototype