A prototype is a model built to prove a concept.
This definition is applicable to anything really, not only games. Most of the products we use every day, from the keyboard I am typing on to the complex machines that can fly outside the Earth's atmosphere and reach other planets, all of these things are the result of endless designs, prototypes, iterations, and failures.
Game prototypes are not meant to be representative of what the entire game will look like; in that case, we talk more about tech demo or pre-alpha development builds. If you have a pre-alpha ready, that means you are at a later stage of the development and you have probably already prototyped your core mechanics to get to the pre-alpha stage. Nonetheless, even at later stages, you might need to address problems that were not obvious before. Maybe finally feeling how your game actually plays in the hands of a playtester—or even your own—raises questions about something you could have done differently or...