Armor weakens how much damage is taken, but does not block a specific amount (so it's not a matter of, say, "50 damage - 30 armor = 20 damage taken", but rather "you take x% [based on the formula pointed out by Pat Fenis] of the 50 damage dealt").

Shields act like a second layer of armor - it works exactly the same way to weaken the damage before it gets to armor, which then weakens that new value further. Small shields ("not-tower-shields") have higher block values when used in a Parry (block action just as/immediately before the attack hits - shields named as bucklers tend to have higher multipliers [x2.5 typically] than ones labeled as round shields [usually x1.5]).

On top of that, some armors will provide a resistance or vulnerability to specific types of damage. A resistance typically halves the damage you take after it's been run through the armor calculation, while a vulnerability typically adds half-again of what got through.

Finally, armor currently also applies to DoT (Damage-over-Time) attacks, lessening the risks of things like fire or poison without needing any specific resistance (as mentioned in the previous paragraph).