Armor is your ship's hit points. If your armor runs out, you will lose your current combat session. If you are in an encounter, you will still be able to watch, but not participate.
If your armor is damaged you can repair it on planets for a small fee, or on Gemini Station for free. Repairs at Gemini are done automatically when you dock with it.
Any damage sustained during an encounter will be repaired for free when the encounter ends.