Nobody likes being shot at. When soldiers are in dangerous or unpleasant situations, they tend to become discouraged and frightened. If they are kept in these situations for too long without a rest, they might very well run from the enemy at their next encounter. Every regiment has a morale rating, displayed onscreen as the blue bar below the company banner. There are some things that will cause this morale to decrease. Simply being in combat causes a slow drain, and having a unit within the regiment killed can cause a significant drop in morale. There are also some factors that will cause a regiment’s morale to increase, such as time away from combat or killing an enemy. There are a great many more things that can cause a regiment’s morale to rise and drop during a battle, and those factors are different for every type or regiment. A commander must be aware of the risks of allowing his regiments’ morale to fall too low. Select a regiment and look at the blue morale bar
under its banner in the information panel. The vertical line in the morale bar indicates the regiment’s breaking point.When the morale of a regiment drops below its breaking point, the regiment will
rout. When a regiment
routs, it assumes column formation and moves away from its enemies. You have no control over it until it has stopped on its own and the regiment is as likely to run deeper into trouble as it is toward safety.

Source: Axis and Allies RTS Official Manual