What are the straw hats for and how does one collect them?

The straw hats are points you need to the get the Barber Chop grand prize for this month's (July 2021) seasonal set. When on your island screen, tap the straw hat icon (3rd on the bottom) to see the grand prize that is offered. Tap "Show" to see your progress bar (see more info below). To collect points/hats, you have to purchase the items listed below the progress bar or obtain the Marvelous prizes from the pink star boxes. Each item has a given number of points/hats shown above the name. The game will show you which items are "owned" (purchased this month, not previously), which are "in construction", and which items you still have yet to get through the "show" button. You can mix and match any of the items to get the necessary points. You do not have to get one of each.

The progress bar shows how many points/hats you need to reach the grand prize. It has 2 color tones, in this case yellow and orange. On the left, yellow is the amount of points/hats you have already earned. Orange is how many points/hats you have "in construction". Once your item has finished construction AND you remove the red ribbon, the points/hats will count toward the total. The number shown is how many points/hats you still need and DOES NOT include the items you have in construction.

While the point system is the essentially same month to month, the icon (straw hat) changes.