I wasn't aware that there are other islands besides the main Orchids Island. When, and how, can you..

When you have 3 plots left to clear on Orchid Island, you will receive the map icon. Once you clear all the plots, the map icon will be your access to the next island, Sunflower Island. After you clear Sunflower Island, the map will give you access to the 3rd island, Laurel Island, and after you clear that, you'll have access to the 4th island, Willow Island.