On each new destination in the world tour, you can earn Souvenirs unique to that destination. Each time you have collected all the souvenirs for that destination you get one of the following rewards: 
First Completion - Passport to next Destination 
Second Completion - Profile Frame 
Third Completion - Diamonds (Varies between destinations) 
Want to get a head start on your collection? You can view a list of Gift Boxes that are purchasable with Diamonds by tapping on the "Get More Souvenirs" button at the bottom of the souvenir page. Each gift box provides a varying amount of souvenirs.