Hidden Goodies are bonus tasks that you can do on an expedition island. Only the first island, Treasure Island, doesn't have these Hidden Goodies. On every other expedition island, treasures of different kinds are hidden for you to find.
You can find these treasures while exploring the island. When you find all the goodies, you will earn hefty prizes.
While finding these goodies mean you will get sweet prizes, it is not mandatory to do Hidden Goodies tasks. If you are finished with the expedition island but haven't yet finished with the Hidden Goodies tasks, the game will ask you if you wish to complete them before you leave for the next island. You can either stay in the island a bit more to collect the goods or leave the island without collecting them as you wish.