Metagame comes into play in any game where no single strategy is dominant and opposing sides are aware of multiple strategies that can succeed dependent upon opponents' actions. In order to perform at the highest level, it then becomes necessary to think about what your opponent thinks you will do (which may depend on what he thinks you think he thinks he will do, etc.) and to make decisions based on clues regarding what level they are thinking on.
This term is most commonly used to refer to poker and other complex card games, but is increasingly being used in relation to video games with complicated player vs player elements and even traditional sports.
This guy thinks that I'm going to zergling rush which means he will waste resources defending early. Instead I am going to focus on resource development for mid game, and metagame will win me this match.
The metagame is usually much more narrow then casual gaming, and there is often very little variation in strategy between metagamers because only the best are used.
Metagame often involves strategies found or created by players, not just simple tactics designed by the game developers to intentionally be part of the game, while also playing by the standards other metagamers believe to be commonplace.
Games such as mario bros or freeze tag usually lack a metagame, because the multiplayer aspect is limited, and/or there is little to no strategy or skill involved in the game, simple games in general usually lack or have a very small metagame, while more complex and competitive games usually have a larger metagame and a larger gap between strong and weak players.
Person: "Urgh I hate the meta, there is no originality and I always lose to them, everyone uses the exact same strategy"
In Metroid Prime Hunters, which was considered the best FPS on the ds for a long time, and still is arguably the best*, almost all metagamers would use the imperialist as a weapon, and sylux or trace as a character, most metagamers consider alt forms to be spammy and noobish, because they don't take much skill to use and allow noobs to beat players who do not use alts but have significantly more skill.
*(at the time of this writing)