Character Cards are a special reward you can earn from Star Boxes.
These go into a special scrapbook you can access by tapping the blue satchel in the bottom of the Island screen and then the scrapbook icon.
Collecting sets of Character Cards allows you to unlock new information about Virginia, Sam, Jack, and all of your favorite June's Journey characters. This is a somewhat advanced feature that develops slowly over a long time, so we're not going to spoil the surprises here. Enjoy the stories!