An Incarnation is a sapient, though not necessarily sophont, embodiment of a concept; the "monster in the machine" as referred to by others. It is an idea given life and thus unkillable with weapons. It is supported and fed through certain ideas, and you defeat it by taking the strength from that idea. Most often, people simply accommodate them.
An incarnation comes into being when a person summons and melds into it. Multiple copies/versions/emanations can exist concomitantly and even absorb the lesser versions of themselves for strength. They cannot go against their nature as incarnations with out a loss of power, which makes them somewhat predictable. They can absorb other people to gain power and evolve their concept, to be able to break from what they embody. They are a singular idea, they can not be as complex as a country but there can be nuances to them, like the difference between conquest and war.
They are the type of Other that can become powerful enough to affect the area they inhabit as a sort of pseudo-Demesne.
↑“The Lord is an incarnation of Conquest. He’s a sapient embodiment of a concept, and he’s been here for some time, in one form or another.” [...] “A living manifestation of conquest?” I asked.
“I would hesitate to say ‘alive’.”
“He’s the horseman? One of the four riders of the apocalypse?”
“Yes and no. There are other Conquests, who take different forms based on their history and the eras and events they drew power from. For all intents and purposes, you can consider incarnations to be powerful spirits, often ones with human hosts or an attachment to an object of particular design, an implement without an owner. Some agencies contrive to bring these incarnations into being to suit their devices. Is there an agency invested in the apocalypse and Conquest’s part in that? Yes, but not in the way you’re thinking.”- Excerpt from Collateral 4.1
↑“And nobody’s about to remove the local Conquest from the picture, to keep that from happening?”
“There are bigger things at play, and an Incarnation isn’t a monster you defeat with a sword or gun. It is an idea given life. You support it and feed it through certain ideas, and you defeat it by taking the strength from that idea. Most often, you accommodate them. But anything powerful enough to become sentient and sapient isn’t something that’s going away anytime soon.” - Excerpt from Collateral 4.1
“He isn’t War, but Conquest. Massed forces, takeovers, forced change. He continues to find power in other ways. Yes, he prefers warfare and bloodshed, but he can draw power from the steady expansion of civilization into nature, from real estate, from business takeovers, government, law, and other small forms of tyranny. As an Incarnation, he can invest his power. Where Death might bring death to things by touching them, or Love might strike a couple through their hearts with a metaphorical arrow given form, Conquest can do the same.” - Excerpt from Collateral 4.1
↑“To be in Conquest’s domain is to be in a constant state of transition. Emotions rise and fall, there is fire and rebellion at first, then we make peace with the state of things. Broken things erode away, and then there is only defeat. But to be the Conqueror is not a simple thing either. They either take on a different role, which my lord cannot do, or they find new territory to seize, people to subjugate. The territory changes as he finds new ground.”
“I didn’t know a demesne could be this… out there. I mean, I read about apartments covered in flesh, but…”
“This isn’t a demesne, as you understand the term,” he said. “Some beings are strong enough to influence their surroundings simply by residing there.” - Excerpt from Collateral 4.2