It was a feature on gen 5 and 6 that had the duration of the gen to access. It included the dream world during the gen 5 era, but that's all I know about it, because I didn't play much of gen 5 during the time it came out.
In the gen 6, you could play minigames, that gave out numerous rewards, using you pokémiles after syncing you game. You could also use them to buy items like max revives and rare candies in a shop that had half the price of those in-game, and during the last 2 weeks of the gen 6 service, the price was halved another time for all shop items and atractions, so you could buy a rare candy for 125 pokémiles instead of 500.
Overall it was a pretty cool service. I just wish the commemorative medals went through like it happened in the gen 5 -> 6 passage.
You can have a look at it in here