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, are a duo of two overzealous investigators: Ken (ケン Ken) and Mary (メリー Mary). They are recurring characters in the Pokémon anime.
The duo first appeared in Wish Upon a Star Shape. A spacecraft carrying a group of Clefairy 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.
The PMC duo were determined, though they were competing against the equally stubborn Team Rocket trio for Cleffa. Ken and Mary eventually clashed with Jessie and her teammates in a robot mecha battle. The Clefairy saw an opportunity and promptly recycled the two machines, using the spare parts to repair their damaged spacecraft. Pikachu sent the PMC and Rocket trio blasting off with a mighty Thunderbolt. Phanpy did its job perfectly, and the Cleffa later evolved into a Clefairy so it could get on board the spacecraft as it flew away.
During another mystery, Ken and Mary were investigating the source of crop circles in some fields. They discovered the source was actually a Snorlax who went on to squash them as it rolled over in its sleep.
In Crazy as a Lunatone, the PMC traveled to the Hoenn region following a meteor strike near Volley Town, in search of another Extraterrestrial Pokémon. Ken and Mary's suspicions were correct, as a Lunatone emerged from the crater site. However Lunatone escaped them the first time by wiping their memories.
They confronted Ash and his friends as they were enjoying a meal. Ken and Mary prepared to take Brock's Lombre away for further study, thinking it was an extraterrestrial Pokémon. However, Max was quick to point out that Lombre was actually the evolved form of Lotad, and Mary confirmed this with her Pokédex. The PMC duo were somewhat disappointed, but quickly rushed off in search of Lunatone.
The group and Nurse Joy did their level best to transport the Lunatone to Camerupt Point so it can return to space, but the PMC arrived on the scene. Ken and Mary's latest machine blasted the Rocket trio off by exploding, and Lunatone used Hidden Power to send them to their same fate as well. Ken and Mary are never seen again for the entirety of the series.
The goal of the PMC is to do whatever it takes to conclusively prove that Pokémon are extraterrestrial lifeforms, which causes them to be motivated into capturing Pokémon species which have relations to outer space, such as Cleffa and Lunatone for further study.
Like Team Rocket, they have a motto but consider themselves to be heroes, despite their dubious methods. Although they don't have Pokémon of their own, they have a variety of scientifically-advanced equipment and gadgets, including bulldozers, jetpacks, robots, rocket launchers, and a Pokédex that only tells the basic info which they build themselves using tools from the suitcase that Mary carries.