Eluka is the alternate dimension that Kazuya enters in his search for the transcendent realm that the Nova come from. To Kazuya, it appears as a midevil world similar to a fantasy RPG. There he meets Satellizer Alexander Eluka, a doppelganger of Satellizer and Maria Eluka Nova, considered the Goddess of the world, Holy Mother, and a doppelganger of Maria Lancelot.
The world of Eluka seems to be matriarchal. It's population is mostly female with Maria Eluka ruling as Goddess over the Holy City and a number of noble families. Males are stated to be extremely rare. Ibanyle, the High Priest is the only one male being seen. Also it is hinted that all males are born with the power of Freezing, or better known as Compassion Link as it is called.
It is revealed that Eluka is the transcendent realm where human souls go after death where they lose their emotions and sense of humanity. The reason it appears as it does is based on Kazuya's perception, forming the world in a way he can perceive and understand.
Eluka is ruled by the Goddesses of Balance which are known to be Nova. They have ruled Eluka for years and one of the Goddesses, Erectar Eluka Nova is the head ruler of Eluka controlling the world under her will.