Pokémon X and Y/Pokémon-Amie

Pokémon-Amie is a new feature that lets you interact with your own Pokémon. It can be accessed at any time from the bottom screen, available as soon as you obtain your first Pokémon. Pokémon-Amie is the only way to build up your Pokémon's affection, an optional statistic that gives tons of benefits in in-game battles, from increased experience gain to the ability to shrug off status ailments.

The three main stats
There are three special statistics specific to Pokémon-Amie, which can be viewed by pressing the "switch" button. Affection is the main stat that actually has an effect in battles. It reflects how much your Pokémon likes you, and determines the benefits you get in battle. Affection must be raised by either rubbing your Pokémon or giving it Poké Puffs. Affection cannot be lowered and is not related to a Pokémon's friendship.

Fullness is obviously how full your Pokémon is. It is raised by feeding Poké Puffs to the Pokémon and lowered by playing minigames with it or after a set time. If a Pokémon is full enough, it will refuse to eat any more Poké Puffs until its Fullness is lowered again. Enjoyment is how happy your Pokémon is. It can be raised by playing minigames with your Pokémon, and is lowered by rubbing the Pokémon or after a set time.

The main screen
On the Pokémon-Amie screen, you can select wallpapers and decorations to place around your selected Pokémon. Frequently, there will be Pokémon from your friends, acquaintances and any passersby that will show up on your Pokémon-Amie screen. They will often leave more decorations as well as Poké Puffs for you once they have left. You can also gain decorations by playing with your Pokémon.