Diamonds are a precious resource in Best Fiends. They are mainly used for growing your Fiends when you do not have enough Meteormites for an upgrade or for buying Keys that you can use to open the crates to find Meteormites, more Diamonds, Energy or Fiends!
If you do not have enough Yellow or Blue Meteormites to grow a Fiend, the game will ask if you would like to make up for missing Meteormites by spending Diamonds to complete the upgrade.
You can purchase more Diamonds from Brittle's Diamond Store, which can be accessed from the top-right corner of the World Map by tapping on the Diamond icon.
You can also gain extra Diamonds for free by collecting them in some levels, participating in game events, by watching an ad to spin the Fiend of Fortune, by using the Keys, or from Gifts from Facebook friends.