The Zoid Eve is an Ancient Zoidian relic found in the ancient city of Evopolis, which is buried in the Valley of the Rare Hertz. It is the power source of all Zoids, and its functionality directly affects that of all Zoids on Planet Zi. It was sealed and powered-down by the Ancient Zoidians when the Death Saurer went berserk in the ancient past.
This, in turn, allowed them to seal the otherwise unstoppable Zoid, though it also led to the other remaining Zoids losing some of their power, as well. The Zoid Eve does not appear in any other anime series, nor is any reference made to it (though locations near it are mentioned in Zoids: New Century Zero). It is noteworthy, however, to mention that Reggel is stated to be the power source for Zoids in Zoids: Genesis.
Fiona mentions Zoid Eve in passing, and Van, trying to recover her memory, seeks out this mysterious place, knowing nothing about it but its name. This started off his journey and hence, the whole series. Gunther Prozen, however, was the only one who actually knew anything about the Zoid Eve, and he expended a great deal of effort in (covertly) researching and excavating ruins across Zi, eventually resulting in the resurrection of a cloned Death Saurer.
The Zoid Eve is finally shown in full in the climax of Guardian Force, when Prozen, fused with the Death Saurer's still-alive Zoid Core, took Fiona and made her utter the password to the Ancient Zoidian city of Evopolis. This password was revealed to be "Fiona" (her actual name is "Elisi Linette", Fiona is the name given to her by Van in the previous series, when he mistook the password for her name), and it revived the Zoid Eve. It also revived the Death Saurer, which fused with the Zoid Core of the Death Stinger, and became far more powerful than the previous clone employed by Prozen. This prompted Fiona to try and use Zeke, along with her Ancient Zoidian heritage, to destroy the Zoid Eve, thus killing every Zoid on Zi, including the rampaging Death Saurer. While this would save the humans, Van felt this too great a price to pay, and came up with a different strategy. He is ultimately able to defeat the Death Saurer by firing his Blade Liger out of the Ultrasaurus' Gravity Cannon.
Surrounding the Zoid Eve is a mysterious electromagnetic field called the Rare Hertz. The Rare Hertz disrupts Zoids and causes them to go out of control. To prevent this loss of control, pilots can install a device called a "Pulse Guard". Organoids, however, lack this Pulse Guard, and thus can go rogue when exposed to the Rare Hertz.
In the Chaotic Century Manga, the Zoid Eve is depicted as being an ancient Zoid that is the ancestor of all Zoids. If a Zoids family tree was traversed, tracing the "parents" of every Zoid, it would eventually end at the Zoid Eve. The manga ends before the Zoid Eve makes a physical appearance.