Metagaming is making decisions made in respect to rules that aren't written, or going beyond the rules of the game. Cheating is a form of metagaming, for example.
In League of Legends, every decision players make is more or less, metagaming. The game doesn't have many of it's own rules, players make them up. The only thing we know for sure about the goals league of legends is that players need to destroy the towers and eventually the nexus to win. How one can go about doing that is completely up to the players. Riot gave us pieces and a goal, how we use them is the metagame.
The term metagame does not necessarily relate to pre-written strategies (although with enough play by enough people, it certainly can). The term originates from Dungeons of Dragons. If you've ever had a guy go "I want to roll a d20 to determine whether or not I can jump over the chasm, pull out the knife no one knew I had, and cut the rope to save my team entire team and deal damage to the boss" you've had someone metagame. This example is metagaming because this guy is (attempting) to do more than is reasonable in a single turn, attempting to use mechanics and actions that don't necessarily exist in (or at least aren't defined by) the universe he's in.
In League of Legends, an simple and very common example might be where certain champions go for the purposes of laning. There's no reason Xerath and Katarina can't go bottom together, mechanically: this decision was made because of data the Xerath player has from external sources. This information is on a level above the game itself, thus the word: metagaming. The mistake people seem to make a lot is that this is the only definition for the word. There are plenty other examples of metagaming in League: items bought by certain champions, decisions about how to path through the jungle, when to go for objectives, and much more. None of these things are forced on you by the game itself, you make these decisions based on things you know (or think you know).
As you can see, the definition is very open-ended, and because of the multiple ways one can metagame, it's a tough word to actually define. I'm OK with having multiple micro-definitions for the word.