Manifestation (顕現 Kengen) is the materialization of Crimson Denizens in the human world and the New World Xanadu. It also refers to how the combination of someone's intentions, mental image, and the use of Power of Existence, can materialize substances and Unrestricted Spells.
Background[]
Essentially, Crimson Denizens, Flame Haze and Torches all consume Power of Existence in order to manifest, though there are some exceptions. One example of this would be a Denizen that was on top of the Treasure Tool Caina; as long as one stayed on Caina, their manifestation would continue without consuming Power of Existence.
Another example is Dantalion, who possessed a unique ability that set him apart from typical Denizens. Normal Denizens could only produce phenomena such that were just temporary interference, like fire or wind. On the other hand, Dantalion's power utilized manifestation, which is normally a materialization of oneself, and imposed it onto substances; this enabled those substances to materialize as other objects permanently. Due to this, Dantalion's inventions stop functioning but do not disappear when he was destroyed. However, it is possible reactivate those inventions or salvage some of the function: Yūji Sakai manages to make Dragon Tail and Tyrant operable again in Xanadu after a few years of research, and Cerebus who extracts from Messenger's Dagger an Unrestricted Spell of guidance serving as the exit point for teleportation in an attempt to bring Dantalion to Xanadu.
Tiriel losing her manifestation due to lack of Power of Existence
The Power of Existence used for the manifestation can be used to an extent that the user's body becomes only semi-manifested due to the lack of power. Tiriel is forced to resort to this when she did not have enough Power of Existence to protect Sorath and stop Shana's attack.[1][2]
Crimson Denizens[]
As Denizens originally lacked physical body in human world, they convert their essence (in other word, their own Power of Existence) and materialize their physical body. All actions they conduct within the human world is done via this manifestation.
Flame Haze[]
Flame Haze's extraordinary powers, like the strengthening of their body or the use of Unrestricted Spells, are the manifestation that consume the Power of Existence of their contracted Crimson Lords who lie dormant inside them.
Staying inside their Flame Haze's Vessels that work as "disguises" in this world, these Crimson Lords do not need to consume Power of Existence. For a Crimson Lord who loses their contracted Flame Haze, if they want to remain in the human world, they must continue to consume the Power of Existence like other Crimson Denizens do. For Crimson Lords whose mission is to protect the balance of the world, they only have two choices; either return to the Crimson Realm immediately, or use their own Power of Existence and perish when they exhaust it.
Torches[]
Torches consume their remaining Power of Existence and materialize a body as substitute for a human. However, if they have a strong will, and their remaining Flame is strong enough to withstand consumption, they can learn how to use Power of Existence and manifest a body that is beyond a substitute for a human, and even learn how to use Unrestricted Spells.
Gods[]
For Crimson Gods, it is the same as Denizens, except when they are summoned to the human world through a Divine Summoning. If this is the case then the manifestation of the God does not need to consume any Power of Existence from the human world or from themselves.