Your level is indicated by the number next to June's picture in the top right corner when viewing your island. You must increase your level to unlock new scenes and chapters.
To increase your level, you need Flowers. The amount of Flowers required to reach the next level is indicated by the number next to the Flower progress bar, in the top right corner when viewing your island.
Earn Flowers by placing decorations on Orchid Island, by placing and upgrading buildings, and by restoring landmarks. The amount of Flowers a decoration or building awards is displayed with the item in the shop, next to the Flower symbol.
Buildings and landmarks require you to upgrade them in order to receive the maximum Flower value.