What does it mean when you get a portrait in your star box?

These are character cards. Once you collect 7 of the same character, you can complete a jigsaw puzzle, learn more about the characters, and most importantly, get a full bar of energy (110 energy for the regular bar or 150 if you have the extended bar). The puzzles do not expire, so you can save them up and use them when you need them most.

You can access them through the photo album, which you find by tapping on the Estate (4x4) building. If you have coins saved up on the Estate and do not want to cash the coins in, then first open the storage inventory before tapping on the Estate to access the photo album icon. Once you have opened the photo album, tap on the green icon with the grid to access the entire photo book. If a photo slot says 7/7, it means you have the 7 cards ready to complete that jigsaw puzzle.