Morale is a unit ability score measuring bravery in battle. Morale scores are used to prevent squad routing, side routing, and individual checks against specific special abilities - primarily Awe.
Morale can be improved via units with standard, spells such as Sermon of Courage or Fanaticism, friendly dominion, fighting in the province where recruited, being lead by an inspirational commander (may be native to the commander or granted by a magic item or heroic ability) or by effective leadership (For each additional 40 leadership after the first, commanders give +1 morale to units under their command).
Morale can be decreased by complex formations (this malus is reduced by the ability "formation fighter"), commanders leading more squads than they can handle, enemy dominion (reduces morale by 1), enemy magic (terror, panic, frighten, wailing winds, dark skies), or by being near units with the Fear ability.
Certain morale scores cause special abilities.
A morale of 30 (granted to pretenders, prophets, and many demons) signifies a unit that is generally unbreakable, but will flee if the rest of the army is routed. Note that immortal units in friendly dominion will generally not flee even then.
A morale of 50 means a unit is mindless. This unit will not rout, but will dissolve if left without leadership.
A morale of 99 means a unit is berserk. The unit will not rout, but will accumulate a small amount of fatigue every round.