Myron is Jasmine's grandfather and appeared in the episode "Fight for the Light!" He's mainly remembered for helping care for Sparkle when the Pokémon fell ill, and for giving Ash some strategic advice—namely, to battle the Cianwood Gym Leader first before taking on Jasmine, so she'd have time to prepare.
He also plays a key role in validating Janina, Jasmine's apprentice. When Team Rocket tried to steal Sparkle, Janina used her Onix as a makeshift rope to stop them, and Myron publicly praised her quick thinking. This endorsement turned out to be important later: it helped Jasmine trust Janina even after discovering she'd impersonated the Gym Leader and cheated by coating her Onix in wax during their battle.
Content compiled by AnimeList.moe from publicly available sources.