A fantasy role-playing game is a set of rules which detail the odds of success for things that people in a world of legendary heroes can do. The only equipment required is paper and pencils and a set of polyhedralTM dice, (dice with more or less than six sides). One Player is appointed the referee. The referee plays the part of the gods, nature, and all of the people, kings, and monsters. Each other player takes the role of one individual in the world. They make decisions for these individuals, (called heroes), for the rest of the game. The referee invents obstacles for the heroes. The players think of ways to surmount the obstacles. In effect, everyone is writing a legend.
There is no winning or losing, a good story is the goal of the game. The referee could just make everyone, "go directly to jail, do not pass go," if that were the case.
The referee has the greatest responsibility. The adventurers must challenge the heroes without overwhelming them. Each adventure may consist of many pages of background information. The referee must not be frustrated if the players take an unexpected course of action, (maybe wasting an hour of preparation), the same ideas can be recycled into later events. It's reccomended that a few stock themes be used and re-used, and that several unique ones be held back for special occasions.
A basic adventure may start with an initial contact, (called a patron), who will describe the basics of the adventure and usually offer a prise. Some common patrons are: travellers needing escorts, long lost or epic poems, sheriffs who need deputies or posses, or wizards needing rare ingredients. Heroes don't have to wait to be asked, they are always free to explore, conquer or otherwise; the heroes do whateverthe players want!
The combat system is meant to be fast, yet detailed enough to add flavor to the players' idea of what is happening. Most of the calculating involved in the game is done between encounter, keeping work required during encounters to a minimum. The same basic system is used whenever a hero tries to do something, whether it is climbing a sheer cliff or bargaining with a shrewd merchant. The magic system is slightly different, since it assumes the hero's imagination is a force capable of directly affecting reality.
I read somewhere that "Polyhedral" is a trade mark of TSR, makers of D&D products.