Moe runs Beach House Moe, a struggling restaurant in Porta Vista that's being crushed by the competition—specifically Brutella's more popular place next door. When Ash and his friends accidentally smash their boat into Moe's pier, things go from bad to worse. They try to drum up business using their Pokémon, but Team Rocket and Brutella keep sabotaging every attempt.
Misty enters a local beauty contest, figuring if she wins, the prize money could help Moe rebuild. Team Rocket, naturally, decides this is the perfect moment to cause chaos—they show up with a Gyarados submarine ready to level the whole town. Ash steps in with Charmander and Pidgeotto to send them flying, and they crash directly into Brutella's restaurant, which is basically poetic justice.
The ending depends on the version. In the dub, Ash uses the town-saving reward to fix up Moe's pier and then takes off to travel the world. In the original, the beauty contest prize goes to the winner (strongly implied to be Misty, given why she entered), and she uses it to help rebuild Moe's place.
Moe appears in "Beauty and the Beach" (Episode 18).
Content compiled by AnimeList.moe from publicly available sources.