These mods increase your ship's hit-points. If your armor runs out, your ship becomes critically damaged and will significantly delay your arrival to your destination. Armor hit points, unlike shields, do not regenerate, making damaged ships more vulnerable to attacks from pilots looking for an easy kill. Most armor mods simply pile on hit points but some have unique abilities such as reflecting damage back to the attacker or reducing the damage received.
You can obtain armor mods from nearly every location, but Earth specializes in defensive mods. So, if you want to make sure you’re ship can leave a fight in one piece, focus on building up your Earth reputation.