An Illusion is an unreal being, essentially a Major Image from D&D. It can be made convincing by a Glamour Mage, but only until a weapon or spell effect gets through their Protection and does even one point of damage; then the façade fails, and that's that.
Illusions are all Mindless and Inanimate. They're also Spirit Forms, and thus they're also Ethereal. In the game's lore, this 75% chance for nonmagical attacks to not work on them is explained as them "moving erratically", possibly dodging before the hit lands. Alternatively, other units may be Ethereal, giving illusions a large buffer of credibility for the first few times swords go right through them. Spirit Forms also don't interact with a wide array of magic, most of which is in the school of Alteration.
Illusions have "Phantasmal" Weapons, which are also unreal and do False Damage. In prior games, this was regular damage that Magic Resistance would negate. In Dominions 6, this is damage that persists as long as the person who has it believes it to be real, effectively up until the Glamour Mages and/or Glamour Manipulators facing them leave the field. As a tradeoff with its state in earlier games (no longer being blocked by Magic Resistance), the attacks of Illusions are all rather weak in power, with a base damage of 1.
Note that, technically, not everything an Illusion does is unreal. For example, Projections cast by Project Self are spellcasters with the same capabilities as whoever made them, and their spells are quite real. Interestingly, Projections are also Mindless, so the maker of a Projection is in absolutely no danger while terrorizing their foes.
Disbelievers are not fooled by Illusions and may call them out; this results in a Magic Resistance check for each Illusion, followed by separate DRNs to determine whether or not each Illusion takes "fatal" (1) damage. For the latter checks, the Disbeliever wins ties.
Disbelief functions like an aura, intermittently flashing adjacent squares (or sometimes the Disbeliever's square). A higher value indicates a greater chance for flashing, and thus a greater chance to flash a square with an Illusion in it. As with all auras, if the trait value is 25 or higher, there's a small chance that the aura may reach out two squares beyond the Disbeliever; the Bodhisattva of Mercy has a Disbelieve value of 25, for example, though she's a Pretender.