Not all Pokémon will be able to Mega Evolve, but the ones that can are able to tap into a reserve of hidden power in the middle of battle. Their appearance will change and their stats will raise, even their typing might get altered, but Mega Evolved Pokémon will return to their normal form after the end of a battle.
Pokémon X and Y will also introduce Super Training, which will allow your Pokémon to level up and gain strength while not in battle. Super Training involves playing mini-games that will increase your Pokémon’s base stats.