For more details:
Why is morale important?
The lower its morale, the higher the chance for a unit to become disrupted and
the harder it is for the unit to recover from disruption (snowball effect!). Disruption is bad as it halves your unit's combat effectiveness and - most dangerously - makes your unit automatically retreat if assaulted, which can mess up your combat line (zones of control) and might also lead to horrible casualties (if your retreat paths are blocked by enemy ZoCs/units).
Other than disruption (which is absolutely essential), morale doesn't seem to matter much as far as I can see. Many things are based on "unit quality" (=the unit's maximum morale level), not its current morale level
These circumstances reduce a unit's morale:
- disrupted/broken (-1)
- isolated (-1)
- low ammo (-1)
- no fuel (-1)
- fatigue (-1/-2/-4 for 100-199/200-299/ 300 fatigue respectively)
As you can see, isolating units is probably the most effective and quickest way to decrease a unit's morale and thereby increase its disruption chance: -1 isolated, -1 for low ammo (if the unit opportunity-fired at you).
To increase your morale (and thereby also increase the chance for your unit to recover from disruption), make sure to get rid of these negative statuses. A reduced morale value is always temporary. As soon as the negative factors are gone, morale automatically goes up again.
Note however, that the maximum morale level that a unit can have depends on the unit's quality - the unit's maximum morale level is actually refered to as "unit quality" in the manual. How can you tell? If the unit already is at it's maximum morale level, the morale information on the unit card will be displayed in white, if not, it is displayed in yellow.