Black pearls are a very valuable currency that can be used to buy hats for your birds. You can collect black pearls through rewards in the game. Hats give an additional multiplier to your birds and the more pearls the hat costs, the higher the multiplier.
When you are able to collect all of the hats from the same set, your slingshot will be upgraded and it will also give a higher multiplier to your overall score.
Even if you have a very valuable hat set, it is worth going back to purchase those cheaper hat sets to boost your slingshot.