Eternals are truly unique creatures in the Boktai universe. They are not living, dead, undead, or even Immortal- they just exist. Because of this, Eternals are impossible to kill, and so are feared by all, even the Immortals. As of Lunar Knights, only two Eternals have been shown (Jormungandr, the Doomsday Beast; and Vanargand, the Beast of Destruction), and it is unconfirmed if more exist, although it is probable.
While it is unclear, certain details (such as dialogue delivered by Zazie) seem to indicate that the Eternals were the first beings in existence, and that they gave off "seeds" of "being" and "anti-being" that gave rise to life and Immortals. They may also have been responsible for the division of humanity into the Solar and Lunar children, as Jormungandr and Vanargand (and thus, in theory, other Eternals) seem to have power over sunlight, moonlight, dark matter, and the four elements.
Eternals, however, seem to be only faintly sentient and have little to nothing in the way of reason, as Jormungandr sought to devour everything around it and Vanargand sought to destroy anything it came across, both of them with no regard for anything else or any kind of intelligence guiding the actions. It was likely this trait that prompted and allowed the peoples of the world to seal them away (the Lunar children sealing Vanargand inside the moon and the solar, lunar, and dark children working concurrently to seal Jormungandr underground beneath the ruins of a Sol City and the Spiral Tower). It is also likely this same trait, as well as their other powers, that prompts Immortals like Black Dainn and Ratatosk to see them as potential weapons.