Moria is a Sky Trainer who showed up in the episode "Battles in the Sky!" (XY036). She runs the Sky Battle center at Kalos Canyon and is known for her expertise with aerial battles.
Ash first spotted her mid-battle against another Sky Trainer, using her Talonflame against an opponent's Skarmory—and she won handily. When Ash started training at the nearby center, Moria challenged him to a Sky Battle. He accepted, though he was still pretty green at it. She wanted to use Talonflame against his Fletchling, but her Talonflame wasn't impressed and refused to fight something it saw as beneath its skill level. Moria offered a compromise: if Ash's Hawlucha could beat Talonflame, then Fletchling would get its match. Fletchling was all for it.
The fight didn't go Fletchling's way—Hawlucha lost decisively. That should've ended it, but Bonnie pestered Moria about giving Fletchling a shot anyway, and Ash backed her up. Before Moria could decide, Team Rocket showed up and netted Talonflame. Everyone chased them down with wing-suits, and after Serena's Fennekin brought down the balloon, things turned into a ground battle. While Ash fought Team Rocket, Fletchling actually freed Talonflame before Moria could get to it. This impressed Talonflame enough that it finally agreed to battle Fletchling—and Moria went along with it.
The actual fight was intense. Talonflame dominated early, but Fletchling evolved into Fletchinder mid-battle and learned Flame Charge, which let it keep hitting faster and faster. Talonflame couldn't keep up and went down. Moria took the loss well, congratulated Ash, and headed out.
Content compiled by AnimeList.moe from publicly available sources.