I'm pretty sure that the term "Pokémon Master", would mean different things depending on Games vs. Anime, in the Games, a Pokémon Master would be most-likely defined as someone who has become Champion, and 100% the Pokedex, or just someone who has achieved something incredible. In the Anime however, it seems to be more about caring for your Pokémon, and forming bonds with them, which seems to be what Ash does mostly, he trains and grows with his Pokémon. So, in conclusion, there are many definitions of what a Pokémon Master could be, but in Ash's case, I believe it's about growing as a person alongside your Pokémon, and making friends together, and less about physical achievement, such as becoming a Champion or beating a league.
Source: Knowledge