The original plot of League of Legends, before it was all retconned in 2013, was that it was basically a world tournament for political parties to come together and settle their conflicts in a safer environment where they weren't blowing up the planet with runes (the same things Ryze is trying to gather up now, and more or less an analog of nuclear weapons.) Fiddlesticks was some possessed scarecrow that the Institute of War had locked up somewhere. Brand was a spirit of hate, fire and vengeance that some sailors accidentally awakened and was later sealed by Garen and Lux, and Nocturne was killing Summoners in their sleep or something before he was also captured by the Institute.
The original cast of champions were a mix of native Runeterrans and outsiders drawn from other worlds, the latter being Kayle, Morgana, Malphite, Taric, Nasus and Renekton.
Now that it has all been retconned, most of the champions and their role in the story is up in the air, slowly being put in place as Riot releases more story content. So far, what I was able to gather is it's a mix between heroes - champions who are confirmed to be alive and exist in the present era - and legends - champions who are spoken of in legend and whose existence in the current era (or at all) is vague. For the latter, these are champions like Braum, Bard, Poppy, Kindred and Twitch. It hasn't been confirmed, but that's the vibe I'm getting.