Wulfric runs Snowbelle City's Gym and specializes in Ice-type Pokémon. Beat him and you'll earn the Iceberg Badge along with TM13 (Ice Beam). He's known for being genuinely kind to Pokémon—trainers in places like Pokémon Village have a real soft spot for him because of it.
When you first try to find him in Pokémon X and Y, he's not actually at the gym. Instead, he's out at Pokémon Village west of the Winding Woods, where he gives you the lowdown on the place before heading back to his gym to face you. Apparently he's a huge Brycen-Man fan (the show Gym Freaks covered this) and reportedly keeps a photo of his most beloved Pokémon in a locket he wears.
In the anime, Wulfric made his first appearance battling Ash for the eighth Kalos badge in "All Hail the Ice Battlefield!" Despite using only two Pokémon against Ash's three, he won—and afterward told Ash straight up that his real problem wasn't his team, but his lack of trust in Greninja. That hit Ash hard.
Ash came back for a rematch in "A Real Icebreaker!" and this time things looked different. They traded Pokémon until it came down to Greninja versus Abomasnow. Greninja's Ash-Greninja form had the upper hand until Wulfric Mega Evolved his Abomasnow. Even so, Ash managed to pull out the win and finally got his badge.
He also showed up briefly when Ash was reflecting on his Kalos gym victories, and later appeared in the Winding Woods during Lysandre's broadcast. He helped take down the Megalith Zygarde in the final episodes.
Content compiled by AnimeList.moe from publicly available sources.