It is not possible to make the island bigger, however, as you progress in the game you will be able to unlock new areas of land by using badges, coins, and compasses.
To unlock new areas, click or tap on the respective clouded area.
A pop-up will appear listing the requirements to unlock it.
Note: To unlock the different areas on your island you will always need a combination of badges, compasses and coins. You can collect compasses as rewards from playing hidden object scenes or by purchasing them for cash on the "Explore Region" requirement screen. Once you obtain these requirements, you will need to manually tap on the clouded area to unlock the land as it does not automatically occur.