The metagame, as the prefix meta
indicates, is the level above the game - where you make choices relating to how you play the game based on information outside of the current game.
The best example, which was used by Richard Garfield in the Duelist magazine was that of a group of people he used to play Diplomacy with. A certain player would regularly break deals he made during the game when it would benefit him. Now, that's considered a legitimate part of the game. However, because he had a habit of doing that, people stopped making deals with the player. Now, they were operating on information outside of the game itself when making decisions about the gameplay.
This became a very big part of tournament play for Magic: The Gathering. Because your performance at a tournament could vary a lot depending on the type of deck you played and the types other people played, people started doing what became known as "playing the metagame" - they would try to find out as much as possible about what kinds of decks people were playing, then make decisions based on what they expected to see being played. It reached the point where playing the metagame well - guessing the deck types that would be there correctly - would have a much bigger effect on the outcome than actually playing the game itself would.
I have recently started what could be called playing the metagame for Clue. Recently, I and a bunch of my friends have been on a kick, playing a lot of Clue Master Detective. I've reached the point where I've been observing their strategies and how they derive information from the game play, and I've been making strategic choices based on the knowledge I've gotten from after-game discussions, attempting to throw them off. It's actually worked - I finally won my first game. (I am embarassed to admit that, as I used to consisently win games of Clue, I don't know what happened :)