From David Parlett:
A ludeme is an element of play, comparable to, but distinct from, a game component or instrument of play. Kings, queens, bishops, knights, rooks, pawns, and a chequered board, all constitute the instruments of play or the components of the game of Chess. Ludemes are the conceptual elements of the game, most typically equivalent to its "rules" of play. For example, whereas the material piece shaped like a horse and designated "knight" is a component of the game, the distinctively skewed move of a knight is a ludeme of the class "rule of movement". But other types of ludemes also exist. For example, the name, referend and associated connotations of "knight" - those of a chivalric courtier - may be said to constitute a thematic ludeme.
A characteristic property of ludemes is their propensity to propagate by passing not only from one game to another (the long diagonal move of the bishop is not unique to Chess but occurs also in continental Draughts) but even between games of entirely different classes. Thus the thematic ludeme of a knightly figure is not unique to Chess but also occurs in card games. Similarly, but perhaps more abstractly, it might be said that whereas an actual chequered board is an instrument of play, or game component, the idea of chequering a board so as to render diagonal moves more comprehensible is itself a conceptual component or ludeme.
In essence, the term is a mix of ludic (as in ludology, the study of games) and meme (as in Memetic Evolution) to describe how some rules or other concepts transfer from game to game.
In videogames, an example of a common ludeme is experience points and character levels. Both trace their origin to Dungeons and Dragons but are now a common feature of social games and massive multiplayer games.