Duplicate Pops! are used to upgrade the Pop! characters you've collected.
You can view how many Pop! duplicates are required to upgrade a Pop! by looking at that Pop!'s meter on the collection screen. For example, if you've unlocked Marty Mcfly, any time you get another Marty Mcfly Pop!, the meter will increase until you are able to upgrade that Pop! to the next Star Level.
Upgraded Pops! have more powerful Supers, which can lead to higher scores and more Power-Ups and coins collected during game rounds.