Metagame refers to the Deck(s) in current competitive use that are having the greatest success. Specifically, when players talk about the metagame (or 'meta', for short), they talk about which Deck styles and strategies are the most dominant in their area of play. Typically, as metagame Decks become more common, Anti-Meta Decks appear in order to counter them.
Being able to exploit the metagame is a critical skill in Yu-Gi-Oh!. People who consistently do well in tournaments such as the YCS all have two things in common: a comprehensive understanding of the meta and the ability to exploit it.