Basically, your armor value affects how much damage is absorbed before it hits, so the higher it is, the less damage you take. Armor type (light, medium, heavy) does pretty much the same thing, but I think type is figured into the value (so a ship with a better armor type will have a higer base armor value) I think.

Shields are not affected by the armor value as far as I know, but as your shields go down, your shield mitigation goes up, which gives you a higher percentage chance of completly ignoring the damage of an enemy attack. So, for example, at 65% shield mitigation, the enemy's attack has only a 35% chance of getting through and hurting you.

This all just me talking out of my ass though. Whether all this is true or not I don't know, but I'm pretty sure most of its correct.