So we've had explanations given for how the different kinds of magic work in Eorzea; white magic draws on the aether from the surrounding elements, arcanima uses geometric designs, etc, etc. We even have pretty in-depth histories on most of them. Summoning was created by the Allagans during the Third Astral Era to combat Meracydia, Black Magic was developed by Shatotto during the the Fifth Astral Era...
However, the nature of the dark magic that Dark Knights harness is... incredibly vague. As far as history, we don't have much. The first dark knight turned against a corrupt clergyman and was stripped of his titles and denounced for it, only to cast aside his shield and "in its place, he came to wield something far more potent: a power born of the abyss which lies at the heart of us all. A darkness which can grant us great strength...at a price." He then trained two apprentices, and they in turn have their own roles in training the player, making us the third generation of dark knights. So not much to go on in terms of history.
Now, its also not any kind of thaumaturgy. If you talk to Cocobuki in the thaumaturge guild before the lv. 60 quest, he says something along the lines of his art being more arcane in nature than that of the dark knight. After completing the lv. 60 quest; "Hm hm hm... You think darkness is your ally? Be wary, [player], for darkness bears no allegiances.
"There's a darkness within us all - nothing dangerous, mind. In fact, it's quite healthy. But the crystal changes you - gives you the power to channel it." - Fray
And it's more than just channeling aether, there's a definite structure and form to some of the spells that speak to something more complex than just "grrr rawr, anger rage rawr."
So what is it? Void magic? Channeling negative emotions into power via aether, à la the Sith with the force? And by using the darkness within, are dark knights actually using their own personal aether to harness that power instead of the aether of the environment? That'd certainly explain "the price," as anyone who's leveled a conjurer will know.