Armor in Stick of Truth functions as flat damage reduction, per hit.
Thus, if you have 100 Armor, and are hit by an attack that does 1000 damage, you'll only take 900 damage.
The thing that's great about Armor however, is that this applies to every hit, and tons of enemies have basic attacks that hit 2, 3, or even 4 times. So, if our hypothetical enemy, instead of hitting once for 1000, instead hits twice for 500, you'll only take 800 damage. What this means is that as you get hit more often, Armor becomes better and better, relative to just stacking HP; of course, the shorter any given fight is, or the less frequently your new kid gets hit, the more useful HP is instead of Armor. Armor also has the additional bonus that in conjunction with certain weapons, it also adds to your attack, as there are a number of weapons that add, 2, 3, or even 4 times your Armor to your damage.
All that said, I'd generally advise, that, unless you're using one of those weapons with an Armor multiplier effect (which is not a bad strategy! If you stack armor from items and patches, these can be the strongest weapons in the game, and you'll mitigate a ton of damage. It's especially good if you're bad at QTE blocking.), that you not use Armor or HP patches. In general, mitigating incoming damage with blocks is plenty, and patches are best used on either offensive boosts, or on bonuses to regeneration of HP, or PP. You'll generally get much better results.