Jasmine runs the Olivine City Gym and specializes in Steel-type Pokémon, though she's best known for her Ampharos, which she uses to light the city's lighthouse. Her name is a reference to minerals and mining.
In the anime, Jasmine's Ampharos (nicknamed Sparkle) falls ill, forcing her to ask Ash to retrieve medicine from Cianwood City. When Ash eventually returns to challenge her for the Mineral Badge, the battle goes down to the wire—his Pikachu takes out her Magnemite, but her Steelix retaliates and knocks Pikachu out. Ash's Cyndaquil narrowly pulls off a win against Steelix, earning him the badge. What's notable about anime Jasmine is her confidence, especially in later appearances. During their second meeting, she makes a dramatic entrance by summoning her Steelix and then somersaulting off a cliff to land on it. She's straightforward with Ash about not going easy on him.
In the Pokémon Adventures manga, Jasmine's story takes a darker turn. She gets trapped in rubble during an earthquake caused by Team Rocket while fleeing through Ecruteak City. Her Ampharos sends out a distress signal that draws both Gold and Silver to her location, though ultimately Ampharos itself saves her, leaving the two rivals stuck in Tin Tower instead. At the Pokémon League Tournament, Jasmine defeats Brock and disguises her Steelix with rubble to make it look like an Onix—apparently worried that the newly-discovered Steel type would frighten people. She used to specialize in Rock types before Steel Pokémon were officially discovered. Her two Togetics are the parents of Gold's Togepi.
Content compiled by AnimeList.moe from publicly available sources.