When you reach a certain level, you will be able to open one of the Rescue Expeditions. They are located in the Map menu, in the Expeditions section.

These are separate islands, where you can rescue a character that will join you on your main island. Also, here you can replenish your stocks of such resources, as wood, grass and stone.

How does Rescue Expedition differ from the Event Episode?

The event episode is time-limited. Once you start it, you have 25 days to finish it before the event island is closed. Here, you can learn more about event episodes: https://quartsoft.helpshift.com/hc/faq/159-episodes/

Expeditions, on the other hand, are not time-limited, so you can explore them at your own pace. When you complete all the quests, you will get a message that in 3 days, the expedition island will be closed.