Diamonds are in game currency and can be purchased for real money. They function exactly like magic potions except they do not expire. They are used to decompose, refine, evolve, imbue & Patron beast raising. They are currency for purchases from the Depot, Stable, Workshop & Smithy. They also enhance Avalon training, relics & Arena. Finally they can buy insurance policies while selling over the black market.
They can be purchased from the VIP tab on your avatar or by pushing the "+" icon next to the total diamonds on your status bar at the top of the screen. Castlot offers several payment options. Diamonds cost $0.10 USD each and can be purchased in any amount of one of the easy suggested amounts. Castlot offers various 'events' which give bonus functional items, materials, resources and gold for purchasing various amounts of diamonds.
Probably the most important feature of buying diamonds is that your total amount purchased determines your VIP level which gives various permanent bonuses. I would suggest at least purchasing 100 diamonds to reach VIP 2. The cost is $10 USD, which is very inexpensive for a game, but has noticeable advantages over VIP 0 & 1.