If you’re wondering about why you would want to move on to the next island, then you should know that once you fully upgraded and transferred to the next island you can start earning from each of those islands. It may take a while for you to be able to get past the first one, and once you do the succeeding one’s upgrade costs are much higher. As it will take you a lot longer to unlock more islands later on, you should cherish each achievement and know that there are currently 82 islands in Pirate Kings.
By clicking on the options button on the upper left side of your screen, you can visit your islands on the quick link choices available. Be sure to check the previous islands you have fully upgraded as you can hire more pirate crews for that island to increase the daily rewards you can reap from it. From a strategic standpoint though, you may wish to always prioritize trying to purchase upgrades on your current island, and with some leftover gold coins that you would not want to risk being plundered away, you can invest it on the additional crews for the previous islands instead.