Valerie is the leader of the Laverre City Gym. She uses Fairy-type pokémon and awards the Fairy Badge.
Gym Leader: Valerie
Valerie has a level 38 Mawile (weak to Ground and Fire moves), a level 39 Mr. Mime (weak to Poison, Ghost, and Steel moves), and a level 42 Sylveon (weak to Poison and Steel moves). All three have Fairy attacks, and in addition, Mawile has a Dark attack, Mr. Mime has Psychic attacks, and Sylveon has Normal attacks.
When you win, you receive the Fairy Badge, which causes traded pokémon up to level 80 to obey you. Valerie also gives you TM99 Dazzling Gleam.
To go back to the entrance, step on the green warp point in the corner. Then exit the gym. Outside, Shauna and Trevor will show up and ask you to come tour the Poké Ball Factory with them. Go there when you're ready.