A Horror Mark is an unusual presence of magic on a fellow. It's not any magic that they can use to their advantage. Its aura is imperceptible by all but a few, but among the few are some horrible beings.
In common gameplay (without peeking past the curtain of the game's code), Horror Marks appear as a binary. A unit is either branded with UV-visible markers and/or smells beyond the human range (or whatever a Horror Mark really is), or they aren't. A Marked individual can never revert to being un-Marked; they must live with the brand for the rest of their life, including any additional lives they may have or may come into.
In truth, there are degrees to just how Marked a fellow can be. Think of a Horror Mark as a beacon that is visible through at least one layer of existence. If a Marked fellow is Marked again, they essentially have two Horror Marks, though it's still shown as only one. Some spells (such as Astral Geyser) can Horror Mark a fellow more strongly than others; mechanically, this is handled by Horror Marking them more than once. The beacon fades on those who are dead (or at least not in play), for reasons not elaborated on; it decays at a rate of 10% per turn, rounded up, but one Mark will always remain.
The Mindless cannot have Horror Marks. Even if they have heavily subdued personalities (such as in the case of a Vine Man or a Blood Slave), or at least probably have souls (such as in the case of a Golem), the Mindless don't "express" enough to interest the hunters.
The "hunters" of the Horror-Marked are known as Horrors. These Earthdawn entities eat the fears and emotions of beings, sometimes going as far as to consume their souls, though they drink ambient Magic. The Horrors evolved in "good times" when everyone was spitefully irradiating each other with magic, and thus will only detect the Horror-Marked, along with those who attack them.
Quite annoyingly for the Horror-Marked, the Horrors are capable of Horror-Marking fellows with their attacks. They also prefer to hunt targets while they're alone. The more severely a fellow is Horror-Marked (or, in mechanical terms, the more Horror Marks they have), the more likely they are to be ambushed each turn. Thus, one rarely has only a single Horror Mark for the entire game, unless their first Horror kills them.
In certain conditions, Horrors may be drawn to ordinary gem usage as well, due to their powerful discharge of magic; these two situations are the Cataclysm, a Sudden-Death event mirroring Earthdawn's Scourge, and the lesser-but-more-readily-available effect of Astral Corruption.