Caging Hair. It’s the name of the tenth day of the Kohaku route, but here it’s referring to the name of Akiha’s ability.
Akiha is a demon hybrid that “plunders” the heat of any living being that she is able to visually confirm, and Origami is the name for the maximum output state of this ability. Though the plundering is based on sight, if somebody with spiritual vision were to observe it, they would see it as something similar to red threads twining around and consuming the target in a fiery aura. And, at their maximum output, these threads are capable of covering not just the target, but the entire environment the target is in, making escape impossible—thus the name Origami, or “Caging Hair.” During the last day of the Kohaku route, the reason Shiki couldn’t escape from the school building was because the school building itself had been totally covered by Akiha’s Origami.
Against normal people with no spiritual defenses, this is an absolute method of attack, but against somebody like Arcueid whose spiritual rank is on a whole other level, it would merely be a hindrance similar to the world being filled with spider webs. Though, with backup from a sympath it might be able to actually tie her down.
In Melty Blood, it became both Akiha and Vermilion Akiha’s Arc Drive, under the name “Red Lord Origami.” On a side note, the martial arts practiced by the Tohno family are divided into “Blazing Rendition” techniques usable by everybody, and “Red Lord” techniques permitted only to the family head. These are in turn surpassed by the “Crimson Lord” techniques, which are a taboo even among the taboo.

Tsukihime Dokuhon Plus Period: Tsukihime Dictionary Revised