It means you get double Festival Coins from wondertrades.
When you trade Pokemon over either GTS or Wondertrade, the avatar of the most recent person you traded with appears beside the right table inside the castle at the centre of the Plaza. If you speak to them, they will thank you for the trade and you will receive 2 FC, or 4 if the fortune teller has decreed it. The doubling will last the entire Festival Plaza day.