Emergent Gameplay is the principle that complex and/or unexpected behavior arises from the
An artistic rendering of a chessboard minus the pawns.
simple ruelset in a game be it a videogame or a more conventional game like a boardgame.
Examples[]
Chess is a classic example of emergent gameplay. In chess there are only twenty or so rules which include unit movement, win conditions and a few special rules. After the initial few moves there becomes thousands if not millions of potential board arrangements with hundreds of potential strategies that are often generated on the fly and reasoned out many moves in advance.
Another example is the the video game series The Incredible Machine where emergence is the driving design principle behind the series. Each level the player is given an assortment of random objects such as baloons, guns, bellows, and cats and are tasked with a speicfic goal such as getting different kinds of balls into different containers. The games derive heavy emphasis from Rube Goldberg Machines.
There are many more exmaples in the world of games than the two above, but these two illustrate the different between unintentional emergence in the design of a game and intentional emergence. For some more detailed examples see the pages on World of Warcraft and Trading Card Games for a more detailed look at emergence in games.