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A lich is the decayed remains of a wizard that has discovered some way to exist past their natural death. After a lich has "lived" for centuries, the increasingly-irrelevant emaciated corpse it uses for housing the wizard's soul decays to the point where only the skull remains. This much reduced form is where the "demi" part of the demilich's name comes from.
The demilich is several magnitudes more powerful than a regular lich, however, in much the same way an ancient vampire has acquired powers that far exceed its younger kin. Once riled, a demilich will immediately begin trapping the souls of any intruders inside the many gems that comprise the skull. The bodies of the unfortunate targets are instantly teleported deep within the earth or simply annihilated, making resurrections impossible. The skull can only be harmed by specific weapons; those with a high magical charge (say, above +3) and certain anti-undead spells will do a single point of damage per combat round to the skull. The incredibly rare Holy Avenger is one of the few weapons that can cause normal damage.
In video games, the most notable demilich is Kangaxx the Lich, an optional superboss found in Baldur's Gate 2: Shadows of Amn. After the protagonists recover all its golden limbs from various dungeons in the game, it reforms itself and attacks the party - the reward it offers the party is "a quick death". Upon eliminating this initial form, Kangaxx loses its body, becomes a demilich and the battle continues.