The Diamond Case is a feature that allows you to exchange Dog Tags for Diamonds.
The Diamond Case has a number of levels starting with Level 0 and finishing with Level 10. The higher the level, the more Diamonds you earn, however, this will require more Dog Tags to open.

Dog Tags are gathered from earning XP in battles. Every 75 XP earned will give you 1 Dog Tag. Each Dog Tag is worth 5 Diamonds.
After the end of a battle, you can see how many Dog Tags you have earned.

Once you reach a certain number of Dog Tags, depending on the Diamond Case Level, you'll be able to purchase the Diamond Case and earn the Diamonds within.
While Diamond Case level 0 can be opened for free, you must make a purchase to open the Diamond Cases level 1 to 10.

Diamond Cases can be opened early, but you will not get the full Diamond amount if you choose to do so. When you have reached the full number of Dog Tags to open a Diamond Case, you will have 24 hours to open it. If this time expires, the Diamond Case will reset and you'll need to earn the Dog Tags again.