From an actual definition perspective, metagame means all of the strategies that you expect all the other players to use, and how good they are against one another.
There is a perception that LoL has a stale metagame, where there's only ever one dominant strategy at one time. If bruiser junglers are popular, then bruiser junglers are "the meta". If late-game hyper carries are popular, then late-game hyper carries are "the meta". In a healthy game, one type of champion or team would be weak against another type, and as one type became popular, more people would be drawn to its counter. Eventually there would be less of a reason to play that counter because the popular type would become less popular and people would be drawn to the counter's counter.
But because you can't switch to mastering another champion or another completely different team composition at a moment's notice, pro play doesn't have many of these counters. If one professional team is playing the popular dominant team composition, most other teams are just going to hope to outplay them with roughly the same kind of team comp. Mastery is too important; it is difficult and risky to make huge changes to the way you play. People latch onto these copied dominant strategies and assume that they are the only correct way to play, because if there was a better way, wouldn't the pros do that instead? But that's incorrect. It also ignores the fact that what's strong in high level 5v5 play is not necessarily any good in high level solo queue, let alone low level solo queue.
"Meta-" means "transcending". The metagame is the combat that transcends the autoattacks and skillshots that are built into the game. This dance that players do around each other as they try to gain an advantage before they even enter the game. If you are only willing to play what is established as the current best without thinking about what beats that strategy, then you are most certainly not playing the meta.
I hope that I have helped you to grow your understanding of what meta means.