You need diamonds to buy boosters, buy extra moves for levels, and refill lives. More features that you can spend your diamonds on might be added in future updates.

This is how you can get more diamonds:
1. Complete visitors' requests. You receive diamonds for each completed request.
2. Welcome animals to the zoo. You get diamonds as a reward for uniting entire animal families.
3. Buy diamonds in the Zoo Store as an in-app purchase.