The specifics are still kind of murky. The game refers to it was an element (known in Japanese as blue phosphorous water) that returns a high amount of energy for a small amount of mass. It's highly unstable, occurs naturally (in raw form), and evaporates into a blueish haze on contact with air.

It is somehow aetheric in nature, according to the Sightseeing Log,
To power their legions of war machina, the Garleans require a steady supply of the aether-based fuel known as ceruleum.
but several quests in 1.0 made it seem like it wasn't quite as simple as extracting it from crystals, such as when Gridania crystalized the chaotic aether in Toto-rak
But this news of them harnessing the power of aetheric energy and transforming it into crystalline form is intriguing, to say the least. It shows us that the forest city-state still believes it can match the power of the Empire and their ceruleum-driven machina with mere crystals.
or the paranoid bit of foreshadowing that turned out to be more accurate than it let on...
Hm? What do the imperials want with crystals when they got 'emselves ceruleum? Well, ye can't summon a primal with a pot o' blue piss now, can ye?
I've always wondered where that wiki got "extracted from crystals and refined" from. Never did find anything. Maybe I wasn't looking at the right quest in the right language