Diamonds are a type of in-game currency. You need them to buy in-game boosters, increase the amount of moves you get for levels, refill lives, etc.
This is how you can get more:
1. Unlock achievements: the harder the achievement, the more diamonds you receive. Tap the trophy icon in the left sidebar to see the achievements you have available.
2. Earn stars: each one of them gets you diamonds.
3. Connect your game to Facebook or subscribe to our news: doing either one will earn you diamonds.
4. Clean your aquarium and feed your fish on a regular basis, and also help your friends take care of their aquariums. That sometimes earns you diamonds.
5. Open chests: this feature is unlocked once you beat all match-3 levels.
6. Buy diamonds in the Store as an in-app purchase.