Team Flare’s true goal

Well it can raise the affection of the Pokémon towards you. This is achieved by petting the Pokémon, feeding it and playing games with it. You can feed it Poké Puffs, which come in many shapes and colours, and usually the fancier ones will give more hearts towards leveling up affection which is measured in a five-heart scale. Said Poké Puffs are rewards from playing games, with harder difficulties giving better puffs. Your score is also a factor. Playing games burns food given to your Pokémon, so if it's full (turning its head when attempting to feed it), playing some games enable you to feed it more.

Petting it also raises affection, but after a while, instead of hearts, a speech bubble with a musical note will appear, which means further petting will have no effect at that time, it would rather play.

As for the effects: the Pokémon whose affection is higher might display a text when entering battle, like 'your familiar smell is comforting to it' and such. But better yet, these Pokémon might earn boosted experience points, shrug off status conditions (all of them I think), avoid attacks, deal critical strikes and survive an otherwise fatal blow occasionally. Some even evolve with high friendship. To reach the fifth heart after the fourth, you need to level it twice.

Hope this helps.

I'm guessing it has something to do with either Rotom or Cresselia in X/Y (I'm playing X and I got the eerie-hex-maniac-girl-ghost too). The Strange House (at the base of Reversal Mountain) in Black2/White2 is where you get the Lunar Wing to catch Cresselia on Marvelous Bridge (also haunted), and in Diamond/Pearl, Rotom can be found in the haunted Old Chateau in Eterna Forest. I could be wrong of course, it's just a theory. There's still LOADS of stuff we don't know about X/Y yet. It might even have something to do with Darkrai, for all I know. Sorry I couldn't be of much help.