Doubloons are a special currency available in the game which you can receive during your adventures on the distant archipelagos.
While progressing through the archipelago you will occasionally spot a shiny chest:
It will require some provision to reach it but as a reward, you will receive some valuable doubloons which you can later use on your main island in order to purchase wonderful decorations.
To use your doubloons you need to visit the shop menu on your main island and then navigate to the tab with a doubloon icon:
A total amount of doubloons you have will be displayed in the upper-right corner of this tab. Please note that there is a limit on how many decorations of each type you can purchase and place on your island.
More decorations will become available as you will progress through the archipelagos.