This might sound like a strange question, but it's been on my mind for a while. Recently, Riot seems to be taking pains to not ever mention the League or Summoners — some Champions have even had their VOs modified to delete such references. Braum continues this trend. I think that's a bit of a shame: the League provides a fun and versatile "excuse plot" to explain why these Champions are fighting each other. And if you think about it, it's actually got some depth to it: I like the idea of Champions being heroes who sign up to fight, whether to test their skill, win glory, gain favor with those in power, or represent their homeland. You can imagine all kinds of political machinations going on behind the scenes. It also gives players a role in the story, as Summoners. And it allows for conflict without world-obliterating warfare. Some of us have built an entire community-run game mode out of this.
In Braum's case, it seems perfectly natural that he'd want to go fight in the League to help out his village. For example, if he wins some big matches for Demacia, then he might be able to call in favors if his village needs medicine, or protection from Sejuani's raiders, or whatever else. Or maybe he just thinks it sounds like good fun to go brawl with the mightiest heroes of Valoran.
I don't know if you're under contrary orders or not, but if you can, could we just get a post confirming that the League still exists and that Braum is part of it? That request perhaps seems so obvious as to be absurd in a game titled League of Legends, but a lot of people on the lore forums feel like there's some conspiracy underway to retcon what little lore remains and make LoL nothing but all eSports all the time.
I understand that the new initiative is to focus on characters over plot. But I think the League of Legends "excuse plot" actually works well that way: it's a lightweight, simple plot that has a place for virtually any Champion you can imagine. It allows for constant conflict between states without requiring that anyone ever really "win", so it keeps the backstory that new people need to pick up to a minimum.
EDIT: Gentleman Gaston has discovered this Twitter post from Kitae on the topic.