From Bulbapedia, the community-driven Pokémon encyclopedia.
Dr. Moss (Japanese: ドクター・マスダ Dr. Masuda) was a character of the day in Delcatty Got Your Tongue, seen only in flashbacks. He didn't have a speaking role. He is a Pokémon Doctor.
Dr. Moss was Dr. Abby's teacher in the techniques of massage therapy for Pokémon, much like shiatsu. He gave Dr. Abby the Moon Stone that evolved her Skitty into a Delcatty, teaching her that Abby had to 'evolve' herself much like Johnny had.