In general, a term refering to the context and structure within which a game is played, as viewed from a perspective external to the game.
When describing or critiquing a game, metagame analysis covers anything not directly related to gameplay, ranging from spelling errors to discussion of programming techniques.
Metagaming also refers to the use, within the game world, of knowledge gained outside of it. It is thus an explicit breaking of the mimesis contract. Metagaming techniques can include hacking, refering to walkthroughs, consulting hints, or even saving a game before attempting a risky action.
Some games actively discourage metagame thinking. The beginning of Acheton (1978), for example, looks exactly like that of Advent (1976). Experienced players will often realize this, and proceed exactly like they would in Advent, at which point they will die a horrible death.
Others take a more relaxed view, and get silly when confronted with attempts at metagaming. Responses to XYZZY are an excellent example. They acknowledge that, indeed, this is a game, and that there is no way to prevent the user from realizing this.
Still others actually require knowledge not to be found within the context of the game itself. Cheater (1996), +=3 (1994), and many wordplay-oriented works use this technique. These can be said to encourage metagaming.