Basically, your Body Points plus your Armor Points together add up to how much damage you can take. When you're hit by a weapon attack or a spell that does damage to your character, you subtract the damage first from armor, then from body points.
Let's say you have ten body and ten armor. A guy comes at you swinging six normal. After the first hit, you're down to ten body and four armor. A second hit takes down the last four points of armor and does 2 body damage (down to zero armor and eight body).
You can restore armor points by spending one minute refitting your armor (requires blacksmith skill--see pg 58).
A couple more specific notes (pg 96):
--A weapon swinging for the Chaos carrier, a Chaos spell ("I call upon Chaos to cause light/serious/critical/mortal wounds"), or a Cause Damage Gas Poison attack, all cause body damage without affecting armor points.
--Armor is especially important for carrier attacks--if a monster is swinging a weapon where the damage type is an effect of some kind (example: 6 Sleep, 4 Vertigo, 2 Disease), and the damage affects your body points, you take the effect (eg, swinging 6 Sleep, if you have 5 or fewer armor points the 6 will subtract from your body points and you are affected by a Sleep spell).
Hope this helps!