1st trade 3 cards asked by moogle you get a belt for cool costume.
Windurst - Mandra belt
San'D - Rabbit belt
Bastok - Worm belt
All can activate once per day
3 more cards and you got kadomatu (かどまつ | 門松)
New year's decorative pine branches.
if you collect all 7 cards and trade them in, you will get a neck piece with 10/10 warp to the chocobo farm of that nation
PS: Be sure to bring a lot of people to find the missing pieces in the same area. If you have 4 in PT and one of them find the "Soil" spot you will get 4 pieces instead of 1. Also each map has at least one card that's very rare and one that's always there, try to find the missing one from other area and don't waste time finding that rare one. i.e. Ebisu is very rare around teleport-Mea (Tahrongi Canyon) but it's very common in Sauromugue Champaign.
Here are some screenshots:
