A Pokémon master is...
...Someone who genuinely cares for their Pokémon, even if they are just data in a Nintendo DS cart/GBA cartridge/GB Color cartridge/GB cartridge/GameCube memory card/Pokéwalker/whatever else I left out.
...Someone who does not disconnect from battles over random matchup, and will, at worst, forfeit instead.
...Someone who takes both wins and losses gracefully.
...Someone who does not build teams based on what is popular, or by what is the best, but based on personal preference. And still manages to win battles.
...Someone who lives and breathes Pokémon, and could truly not imagine life without it.
...Someone who is called a Pokémon master by their friends, rather than by themself.