Mega Levels are a special type of bonus that is only active while a Pokémon is Mega-Evolved. The more often you Mega Evolve a specific Pokémon, the higher its Mega Level will be. The Mega Level also doesn’t reset when Mega Evolution ends. Note that you can only contribute to an individual Pokémon's Mega Level once per day.
The higher your Pokémon’s Mega Level, the more bonuses that will be active when that Pokémon is Mega-Evolved. These bonuses can affect your gameplay in a variety of ways, for example, increasing XP catch bonuses for Pokémon of the same type as the Mega-Evolved Pokémon.
You can see a Pokémon’s Mega Level, and the bonuses associated with that Pokémon’s Mega Level, by tapping on the Mega icon on its Pokémon details page.
For more details on what actions are required to increase your Pokémon’s Mega Level, and the bonuses associated with that Mega Level, tap on the next Mega Level icon.