The Threefold Model or GDS theory of roleplaying games is an attempt to distinguish three different goals in roleplaying. In its original formation, these are: Drama, Simulation, and Game. It was the inspiration for subsequent theories, such as the GNS Theory, which retained a 3-way division but altered other aspects of the model.
The model
In its most formal sense, the threefold model claims that any single gamemaster decision can be made in order to further the goals of Drama, or Simulation, or Game. By extension, a series of decisions may be described as tending towards one or two of the three goals, to a greater or lesser extent. This can be visualised as an equilateral triangle, with a goal at each vertex, and the points between them representing different weightings of the different goals. As a consequence, a player or GM can characterise their preferred gaming style as a point on this triangle, or in words such as 'mostly gamist' or 'dramatist with a bit of simulationist' or 'right in the middle'. Another consequence of the model is the claim that by advancing towards one of the goals, one is moving away from the other two. Thus a game that is highly dramatic will be neither a good simulation nor a challenging game, and so on. This assertion has been widely challenged, and led to criticism of the model.
The terms
In the terminology of the threefold, the goals of drama, simulation and game have specific meanings.
Drama is concerned with the narrative qualities of the game, such as story, nuances of meaning, exploration of themes, etc. It does not imply following a preset story, but an eagerness to achieve good or well plotted stories and meaning in the unfolding events.
Game is concerned with the amount and kind of challenge that the players face in the course of the game. Ideas such as 'balance' and 'fairness' and 'victory' belong here.
Simulation is concerned with the internal consistency of events that unfold in the gameworld, and ensuring that they are only caused by in-game factors - that is, eliminating metagame concerns. Simulation isn't necessarily concerned with simulating reality; it could be a simulation of any fictional world, cosmology or scenario, according to its own rules.
History of the threefold model
The Threefold Model was widely discussed in the rec.games.frp.advocacy USENET groupin the summer of 1997. Mary Kuhner had laid out many of the central ideas there and John H. Kim had later codified and expanded the discussion. The threefold arose following long arguments and flame-wars about whether one style of roleplaying was 'better' than another style. The name was coined by Kuhner, in a July 1997 post which outlined the principles. In October 1998, a "Frequently Asked Questions" document by Kim on the Threefold Model clearly stated, "An important part of the model is recognising that there are valid different goals for gaming." It has since then been circulated in a variety of places. It was also the inspiration for a related model known as "GNS Theory", which has been articulated by Ron Edwards on the roleplaying discussion siteThe Forge.