Undead is a special trait in Dominions 5. It represents a class of unit that can only be lead by special commanders and are susceptible to Banishment and its variants.

Undead generally have at least partial darkvision or spirit sight and high cold and poison resistance. All of them need not eat and are unaffected by disease (they can have the affliction but won't suffer from it). They tend to have high Max Ages that make Decay less effective against them, but despite what the in-game description for the Undead trait implies they can suffer penalties and afflictions from old age.

Undead generally have high Morale, generally keeping them from routing as long as they have a commander with Undead Leadership on their side. Some, such as Longdead and Soulless, are mindless and will never rout; they will instead stop moving and fall to pieces on the battlefield, if left without undead leadership. Note that only some Undead behave like this; many types, such as Lictors and Ghosts, have minds and follow normal morale rules.

Demons are technically undead, but have different vulnerabilities.

From the manual:

Undead units are subject to banishment. Undead and demon units require undead leadership, which is generally conferred by skill in Death magic (or being an undead commander). Zombies aren’t going to take orders from just anybody. A squad that mixes undead and non-undead gets a -1 morale penalty, for obvious reasons.

Being undead grants no inherent protection against fatigue and does not inherently prevent drowning, although many undead also have the amphibious or poor-amphibian special abilities.

In addition to banishment, undead can be targeted by some particular spells like Solar Rays and Undead Mastery. These are under the paths of Death, Astral, Nature, and Water.

Lastly, Undead units are unaffected by any Diseases they have, and typically can't catch them.