http://www.gamesradar.com/pokemon-x-and-y-review/

"Pocket monsters that have high affection for you (as gained by minigames and the newly added ability to pet your Pokémon) will simply perform better--they'll dodge attacks and land critical hits and shrug off status effects more often. Having your Sylveon survive not one, but two attacks after being at one hitpoint just because it loves you so damn much makes a compelling case for being friends with the little guys. "