Islands is where you do you select your battles and gain resources. You will discover more and more islands as you gain dominance. There are defended and undefended islands. Any island of yours is defended as long as a Hero is placed on it. Islands with no Heroes on them are undefended.
Defended islands are only lost when another player actually beats your defense. The Hero which defended this island is then returned to Mount Olympus. Having a strong defense makes it less likely to lose your defended islands as your base becomes harder to beat. Undefended islands are regularly taken by new opponents for you to fight. This happens automatically without them having to beat your base in battle. This way, there are always enough opponents for you to attack. The number of islands which you can defend at the same time is limited by the amount of Heroes you have unlocked. Having more Heroes allows you to defend more islands. Defended islands produce much more resources than undefended islands. You should always place your Heroes on islands which produce a lot of Gold, Wisdom, or Ambrosia, depending on what you need the most. Undefended islands produce less resources than defended islands, but the sheer amount of undefended islands you can occupy at the same time makes up for this.
Defense Fleets can be deployed on both defended and undefended islands to protect them from being lost for a certain amount of time. You can still lose battles and trophies you just wont lose the island.