Experience Points (XP) are points earned for catching Pokémon, visiting PokéStops, battling, and completing other gameplay actions. Your Trainer level advances as you gain XP. The amount of XP required to level up increases with each Trainer level. As you continue to level up, you’ll gather rare items at PokéStops and encounter Pokémon with higher CP.
Medals are achievements earned by reaching milestones for distance walked, PokéStops visited, Pokémon caught, and other gameplay achievements. Each medal has three achievement milestones: bronze, silver, and gold. Some achievement milestones unlock rewards - such as an increased chance of successfully catching certain Pokémon type.
In the example image, the Trainer has earned the Bird Keeper medal along with a catch bonus reward for Flying-type Pokémon.
To view your medals:
In the Map View, tap the Trainer Profile button.
Select a medal to view your progress towards the achievement.