Armour
Armour is a rating that measures a character's physical damage mitigation. Every 12 points of Armour blocks up to 1 physical damage per hit. The absolute amount of damage blocked gets closer to the maximum the more damage the hit does; however, the proportion of damage blocked decreases.
Armour rating can be increased by wearing equipment, taking certain passive skills, using spells such as Molten Shell, and drinking a Granite FlaskGranite Flask
Lasts 4 Seconds
Consumes 30 of 60 Charges on use
+3000 to ArmourRequires Level 27Right click to drink. Can only hold charges while in belt. Refills as you kill monsters..
Supposedly the most armour monsters have in the game is about 983.^{[1]}
Mechanics
Damage reduction from armour only reduces physical damage taken. Elemental damage and damageovertime are not affected.
The amount of damage reduction is a function of armour rating and the damage taken. Damage reduction is capped at 90%.
Damage Reduction Factor = Armour / ( Armour + (12 * Damage) )
For example, if you have 1200 armour rating this chart indicates how much damage will be reduced by:
Equivalently:
Net Damage = Raw Damage^{2} / (Raw Damage + Armour / 12) Defense Factor = Raw Damage / Net Damage = 1 + Armour / (12 * Raw Damage) = (1 + sqrt(1 + Armour / (Net Damage * 3))) / 2
Therefore we can conclude:
 If raw damage is much less than Armour / 12, raw damage has a nearquadratic effect on net damage. Equivalently, in this regime raw damage has a nearlinear effect on net DPS if the raw DPS is held constant.
 If raw damage is much greater than Armour / 12, raw damage has a nearlinear effect on net damage. Equivalently, in this regime raw damage has little effect on net DPS if the raw DPS is held constant.
 Against attacks of a fixed raw damage, armour has a linear effect on the number of attacks it takes to deplete a certain amount of hit points.
Another way of looking at it is in terms of absolute damage reduction:
Absolute damage reduction = Armour / 12 * Raw Damage / (Raw Damage + Armour / 12)
So damage from attacks is reduced by up to 1 per 12 points of Armour, which means that the supposed monster Armour cap of 983 blocks up to 77.5 damage per attack. Note that as raw damage increases, the damage blocked per attack increases, but the proportion of damage blocked decreases.
The derivative of this with respect to Armour is
dAbsolute damage reduction/dArmour = ((Armour / 12) / (Raw Damage + Armour / 12))^{2}
Passives
There are passive skill nodes that grant additional evasion or a combination of bonuses including evasion.
Armour
These passives increase armour rating by a percentage.
In the case of Iron Reflexes, armour is increased by an amount equal to total evasion. In exchange, evasion is reduced to 0.
Name  Bonuses 

Armour 

Steel Skin 

Riddle of Steel 

Armour Mastery 

Armour and Evasion 

Leather and Steel 

Cloth and Chain 

Armour and Energy Shield 

Body and Soul 

Faith and Steel 

Iron Reflexes 

Miscellany
These passives are related to armour, but don't fit into any other category.
Name  Bonuses 

Acrobatics 

References
 ↑ VictorDoom (May 10, 2013). "Unique Items List  159 of 159". Official Path of Exile Forums. Retrieved June 27, 2013.