Unit veterancy is the system by which the player's units' experience is measured. Using a particular unit more often in battle will increase its veterancy level. When a unit accumulates enough experience, it gets promoted to a new veterancy level. Each veterancy level has a special icon that shows what verterancy level a particular unit is at.
Veteran units have increased damage and hitpoints compared to regular units. Furthermore, once units reach the second veteran level they will be able to self-heal when idle.