Armor is one of two ship hitpoints. Armor is the 2nd line of defense as you only take armor damage after you run out of shields. If you armor reaches zero, your ship will be incapacitated, increasing your travel time by one and resulting in a cracked cockpit screen. Armor cannot be repaired in flight.
If your armor is damaged you can repair it on any major faction for a small fee or automatically on Gemini Station for free.
Any damage sustained during an encounter will be repaired for free when the encounter ends.