Pen and paper role-playing game
A role-playing game is a form of interactive storytelling where the participants are not in complete control of events. An analogy would be that role-playing games (rpgs) are "playing pretend" but with cause-and-effect rules (see below). Ultimately, the goal of rpgs is to have fun, often emphasized by a "golden rule" in the beginning of the main rulebook. The secondary goals of an rpg are either to accomplish some goal of the player character's (PC) within the story world, or to "win" the game by either constantly improving a PC's stats and equipment, eliminating all opposition, or merely surviving. All of this is mediated by a "game master" (GM).
Basic rpg terminology
The game master (GM) can be compared to an artificial intelligence controlling the functions of the world and it's inhabitants, making sure everything reacts appropriately to the PCs' actions.
A player character (PC), is a character controlled by, but different from, a player in the game. Conversely, a non-player character (NPC) is a character controlled by the GM. Players and GM don't usually control characters outside their own but there are rules that allow for exceptions.
A PC's stats determine what he or she can do according to the rules. Stats are generally sectioned into primary stats, secondary stats, and special abilities. Secondary stats deal with specifics (e.g., skills) and are based on primary stats (e.g., intelligence). Both primary and secondary stats can be modified by advantages and disadvantages applying to specific situations, such as being more (or less) apt with social skills. Special abilities can be thought of as superpowers; they're character-defining abilities that are neither constant enough among character types to be primary stats, nor specific enough to be considered secondary. Special abilities can modify and be modified by primary and secondary stats, however. Specific kinds of magic, advanced technology, or superpowers are the most iconic kinds of special abilities.
Rules
(in progress...)