From Bulbapedia, the community-driven Pokémon encyclopedia.
A Pokémon League Conference is a championship tournament that is hosted seemingly annually in several regions in the anime.
The general structure of each league conference is similar: Trainers must register for the region's Pokémon League before they earn any of the region's Badges, something which they can do at seemingly any Pokémon Center or with a Pokémon Professor, and then must win at least eight of the region's Badges in order to be able to register for the competition.
The tournament competition itself has an opening and closing ceremony, as well as a torch with the flame of Moltres or Ho-Oh that burns during the entire tournament, a reference to the real world's Olympic Games. Each tournament competition so far has been seen to be presided over by Charles Goodshow, the president of the Pokémon League, an analogue of the International Olympic Committee president.
The day after the ceremonial torch has been lit, in some of the regional leagues the qualifying rounds begin so as to weed out Trainers who have gotten the required eight Badges, but are not yet skilled enough to continue, and those who survive move on to the preliminary rounds. In other regional leagues, instead, the preliminary rounds will begin right away, and will continue for several days until the top sixteen Trainers have been decided. At this point, there is a short break in the competition so that the Trainers and their Pokémon may rest, followed by the start of the final rounds.
In the final rounds, most, if not all, battles are Full Battles, with each Trainer competing with six Pokémon on each side. All battles are conducted in the main stadium, and Trainers move up the tournament tree in single-elimination style. The winning Trainer, upon defeat of their opponent, is awarded a trophy by Mr. Goodshow himself, and the following day the closing ceremonies begin.
Only those who win the Pokémon League can officially battle the Elite Four of that region.
List of League Conferences