Armor is the strongest protection you will use, and will typically be what the enemy's weapons are striking most often. The hull will not be struck until the armor has failed, with the exception of an especially powerful cannon hit. There are two armor factors to be concerned with: kilotons and stability. Note that weapon damage is also measured in kilotons, this isn't a coincidence.

Kilotons measures the amount of damage the armor can take before an attacker can strike the hull directly. In example, a corvette has 9,600 kilotons of protection, meaning it will absorb 9,600 damage before you get the dreaded "armor plating has been obliterated" message in the battle log, and the ship is virtually defenseless. Stability affects how much damage each individual attack does to the armor. An armor plate with a higher stability will take less damage than one with lower.

The calculation is done as follows: weapon damage x (100 / stability) = damage done to armor. Suppose my corvette was fired upon by a fighter that could deal 20 damage per round. Since, as you will note, the stability is 119%, the result is so:
20 x (100 / 119) ~= 16.807 damage to the armor. The game will always round properly, and thus the result is 17. So we can see, by investing in quality armor, I have reduced the damage by 3.

Armor is damaged normally by a cannon or battery, but takes double damage when hit by a Single Barrel.