Armor reduces the an amount of the incoming damage dealt on you. The more armor you have, the more the damage is reduced, using the following formula.
Damage reduction = Armor/(Armor+100)
This works for repulsion armour, returning the correct 83.33% damage red.
This also means that you are never invulnerable, however, holding 1422 Tough times will cause a damage reduction high enough to round to 100% (though it should be noted that this is not actually 100%, and it is impossible to actually gain complete damage reduction; you will still take ~0.5% damage with 1422 tough times)
Items that increase Armor include Tough Times, Repulsion Armor, and White Undershirt, among other items found in the game. It can also be increased by leveling up your character, along with basically every other stat in the game.
Confirm: Unlike many games, all types of damage are reduced by Armor in Risk of Rain. This makes Shattering Justice more effective than such a debuff would be in a game where damage mitigation was split between multiple resistance types, such as Physical and Magical. The exact effectiveness of max -25 armor on enemies, however, is unknown because enemy armor values are unknown.