It is a rare gemstone formed from the explosion of an atomic blast. It is used by Uten and Kafka as a test of who is most suited to the name Uten. As Kafka was just previously known as Uten. They bet on the name Uten on whoever can take the fire diamond from Ruri undetected, mostly because they would be killed if they were detected by Ruri.
Kafka and Uten then proceed to try and steal the fire diamond while Ruri was asleep. Both of them failed to find Fire Diamond. It was apparently taken by Arclight prior to the bet of Kafka and Uten to be resized into a ring instead of a pendant, as Ruri had too much pendants anyway. Arclight ordered Kafka and Uten to go to the jewelers to have it cut.