From Bulbapedia, the community-driven Pokémon encyclopedia.
The Pokémon Mystery Club (Japanese: ポケモン不思議クラブ Pokémon Mystery Club), or PMC, is a duo of two overzealous investigators: Ken (ケン Ken) and Mary (メリー Mary). They first appeared in Wish Upon a Star Shape and later reappeared in Crazy as a Lunatone.
Like Team Rocket, they have a motto, but consider themselves to be heroes despite their dubious methods. Although they don't use Pokémon of their own, they have a variety of scientifically-advanced equipment and gadgets, including bulldozers, jetpacks, robots, and rocket launchers which they build themselves using tools from the bag that Mary carries.
Their goal seems to be to do whatever it takes to conclusively prove that Pokémon are extraterrestrial lifeforms, which causes them to be motivated into capturing and stealing Pokémon species which have relations to outer space, such as Cleffa and Lunatone.
The duo first appeared in Wish Upon a Star Shape. A spacecraft carrying Cleffa, Clefairy and Clefable had crashed, and a lone Cleffa had fallen out. Ken and Mary wanted to capture the Cleffa so they could study where it came from. Concerned about what Ken and Mary would do to Cleffa, Ash had his Phanpy take care of Cleffa and make sure it got to its spacecraft safely. Phanpy did its job perfectly, and the Cleffa evolved into a Clefairy so it could get on board the spacecraft as it flew away. Ken and Mary, along with Team Rocket were sent blasting off.
The two also appeared in Crazy as a Lunatone, where they were now trying to capture a Lunatone to study it. Just like the last time, they were sent blasting off without getting any information about the Pokémon they tried to capture.