Morale refers mostly to the emotional state of individual players or teams.
In-game 'moral' hasn't applied to units until fairly recently. When Bungie released Myth units didn't have 'morale' they would obey orders until they prevailed or died. The Project Magma devs added the ability to effect a unit's morale in recent versions of Myth. This is a feature that has to be explicitly added to a map by the map's creator so isn't very common. One way it is used is to add a positive morale to a general or leader unit so that all units within a certain distance will benefit from their proximity by having slightly quicker attacks and faster vetting (gaining 'veteran' status).