Marina's a Water-type trainer from the Orange Islands who hit it off with Misty pretty much immediately—they bonded over their shared love of Water Pokémon and decided to settle who was better with a battle.
The match itself was close. Misty's Goldeen went down to Marina's Tentacruel, but Staryu turned things around. Things got weird when Marina switched to her Psyduck, which was way stronger than Misty's—it could actually use Psychic attacks without needing a headache to trigger them, which caught Misty off guard.
Here's where it gets messy. After her Staryu fainted, Misty threw out her own Psyduck, hoping it would finally evolve. But Ash knocked her backpack into the water, and when Misty fished it out, a Golduck came out instead. Misty assumed her Psyduck had evolved and kept battling. The Golduck beat Marina's Starmie (Team Rocket interrupted before the actual Psyduck matchup could finish), so Misty technically won.
Except. none of it was real. Marina's info about the pink tail meaning evolution was wrong. The Golduck was just some wild Pokémon trying to impress Misty, not her own Psyduck. And as Ash pointed out, Misty didn't even catch the thing, so her "win" didn't really count. Marina realized she'd also won her part of the battle using a wild Pokémon she never caught, which kind of undermined her whole argument about superior trainer skill.
Content compiled by AnimeList.moe from publicly available sources.