A set is a collection of digital pins that follow a particular theme, such as Disney's Mickey & Friends which includes Mickey Mouse, Minnie Mouse, Donald Duck and more. Every digital pin generally belongs to a set and to complete a set, you will need to collect at least one of each unique pin in the collection.
Head to your collection on the bottom bar, under the My Pins tab, to see how many digital pins you currently own. Tapping on a digital pin that you own in your collection will show you which pins you need to complete the set. You can then visit the Shop or trade with other collectors during trading hours to finish your collection.