What are the stars for?

As you play new scenes, you fill stars, which are totaled on your island screen. Each mastered scene gives you 5 stars (25 stars per chapter). They are markers of your game progress and do not decrease in number. As more stars accumulate, more items become available in the store and (in conjunction with compasses) more land can be opened.

The stars can be used to expand the open areas on the island.