You can transfer Poké Miles acquired in your Pokémon X, Pokémon Y, Pokémon Omega Ruby, or Pokémon Alpha Sapphire game to your PGL account and use them in the PokéMileage Club. Use the Poké Miles to play attractions or make purchases at the shop, and you can get items and Berries to send back to your game via Game Sync to help you on your adventure. Items and Berries you can get are different between Pokémon X / Pokémon Y and Pokémon Omega Ruby / Pokémon Alpha Sapphire.
To learn how transfer data between your game and PGL via Game Sync, kindly follow this comprehensive guide from the PGL support page.
How to accumulate Poké Miles**
You can save up Poké Miles by walking around in your Pokémon X, Pokémon Y, Pokémon Omega Ruby, or Pokémon Alpha Sapphire game, by trading Pokémon on the GTS, by using StreetPass with other players of Pokémon X, Pokémon Y, Pokémon Omega Ruby, and Pokémon Alpha Sapphire, and by making Link Trades (online, local wireless communication, or infrared connection) and Wonder Trades with other players as well as by receiving them from participating in Online Competitions.
You can check how many Poké Miles you have saved up on the Trainer Information screen. Open the menu with the X Button and press your Trainer Card icon in the lower screen to check.
Transferring Poke Miles to a Different Game Items*
Items and Berries can only be sent to the Game Card that you were using at the time of obtaining them on the PGL. Poké Miles can be transferred between Game Cards if you have multiple Game Cards registered to a single account. You can even transfer points between Pokémon Omega Ruby / Pokémon Alpha Sapphire and Pokémon X / Pokémon Y. Items and Berries cannot be transferred.
PokéMileage Shop Items
** Source 2