Armor is an attribute that some units will use to deflect certain types of damage.
Types of Armor
Armor protects units from certain types of damage. Lots of units come with two types of armor, such as a Long Sword using shock and arrow armor, as they are meant to kill archers and be equal in fighting other shock damage units (such as an enemy swordsmen), and weak vs pierce damage, such as that done by a Pikeman.
This creates the combat triangle, which gets more complex with each passing epoch. If an enemy gets to a higher epoch faster than you, it could mean dire consequences. For example, if an enemy advances to Digital Age while you're still in Atomic Age - Modern, no unit you own has laser armor, and will easily be overrun by laser-wielding troops as you fight them with outdated guns which are less effective.