The Mindless are goobers without a real will to themselves. Maybe they don't have minds. Maybe they don't have souls. Maybe they're just beings who don't have two cents to give on your Terrestrial reality, or at least on your battle plans.
A lot of beings are mindless. Many are Magic Beings, many are Inanimate, and a fair few are Undead.
The Mindless are dumb-dumbs, or at least act in that manner. They have a nominal 50 Morale, meaning that they only rout in certain situations (such as not having Magic Leadership if a Magic Being); in the event of a rout, they swiftly lose all allegiances and disappear from the battlefield, a process known in-game as dissolving. The Mindless are also tougher to promote to commandership than others, requiring the pricey Divine Name instead of the relatively-cheap Gift of Reason.
On the other hand, the Mindless have many benefits. A great many spells don't work on them. They can't fall asleep, they can't be confused or enraged (and they definitely can't be tricked to death with false damage), they don't have the sorts of emotions that draw horrors, they're tough to derail from spellcasting, and they definitely can't be seduced. Granted, there are a few beneficial spells that don't work on the Mindless; aside from Gift of Reason, there are the various rage-based stat-boosts in Fire magic and Nature magic, and they can't use Magic Duel. These are relatively few, however.