I did a bunch of searching on the forum and couldn't find a well-documented place for this, so I figured I'd do the research and write it up. Better to light a flamethrower than curse the darkness, right? Here we go. Note: this whole post is kinda a spoiler, though it'll more just confuse you if you haven't gotten to the relevant part of the game.
When you complete the Charwood-area quest, "Destined for great things", you rescue two of the townsfolk, Fayvara and Falothen, from the clutches of the goblins. To thank you, they offer to teach you new Skills called "Proficiencies" - Fayvara in armor, Falothen in weapons.
These new skills are part of the same skill list and menu that you spend Skill Points in, except they're "hidden" - this training is the only way you can gain these abilities. It's kinda like Ulirfendor's "Shadow Blessing" skill, in that you have to gain it through a quest. Unlike that one, however, once you've gained the first level in a proficiency, you can then spend additional skill points to level it up.
There are 6 Weapon proficiencies (dagger, 1H sword, 2H sword, axe, blunt, and unarmed), and 4 Armor proficiencies (shield, light armor, heavy armor, and "unarmored"). Each proficiency can be leveled to Lvl 3, except for Shield (lvl 2) and Heavy Armor (lvl 4).
Each NPC will teach you one level in one Proficiency as a thanks for rescuing them. They'll then offer to teach you the first level in another Proficiency if you bring them two Oegyth Crystals (there's 8 in the game), and 6000 GP (Fayvara) or 5000 GP (Falothen). So you could unlock up to 4 additional proficiencies, between the two NPCs, if you went out and gathered all the crystals. The additional teachings can't be used to level up an existing proficiency.
Affects & Effects
Pulled from the source code (here's the values, here's where they matter), here's what those abilities do.
Shield (any): +1 Damage Resistance when equipping a shield (e.g. the Wooden Defender will now give you +2; you get no bonus if not wearing a shield).
Affects: Anything in sizes 'Light' or 'Std', in all 4 types of armor (Head, Body, Feet, Hands - but not shields). For body armor, this includes categories Hide Armor, "Armor, leather" and "Armor (Light)".
Effects: For each light armor worn, +30% Block Chance to the base BC of that armor, rounded down. If a you're wearing Fine Snakeskin Gloves, +6% BC, then your bonus from that item is 6% * 30% = 2.4% => 2%.
Affects: Anything in 'Size Large', in all 4 types of armor (Head, Body, Feet, Hands - but not shields). For body armor, this includes categories Splint Mail, Chain Mail, Plate Mail and the generic "Armor (Heavy)". This also includes Heavy Metal headgear, gloves and footwear.
- For each heavy armor worn, +20% Block Chance to the base BC of that armor, rounded down.
- For each heavy armor worn, -25% to any Action Point penalties (for Move or Attack) imposed by that armor, rounded down. Because of the rounding, the only impact this has is if the player levels this skill up to Lvl 4 (by spending 3 more skill points) to fully eliminate the AP penalty of their armor. Or Lvl 2 with Stone Cuirass or Shadowstalker armors, to eliminate half of their 2 AP penalty.
Naked: +10% Block Chance to your player, if not wearing any armor (shields excluded) that has "weight". Item categories without weight include cloth armor, cloth headwear, cloth gloves, and (sounds like a poor idea) cloth footwear. Wear anything else, and you lose your 10% BC bonus.
Note that his proficiencies only affect weapons in your "main" weapon slot. Dual-wielders can, apparently, pound sand.
Affects: Only weapons belonging to the category of proficiency you have gained. This means:
Dagger: Anything in category "Dagger" or "Short Sword"
One-Handed Sword: Anything in categories "Longsword", "Broadsword" or "Rapier"
Two-Handed Sword: Only things categorized as "Two-Handed Sword"
Axe: Anything in "Axe" or "Greataxe" (2H Axe) categories
Blunt: Anything in categories of "Club", "Quarterstaff", "Mace", "Scepter", "Warhammer", or "Giant hammer" (2H Hammer)
- +30% Attack Chance to the AC bonus from that weapon, rounded down. This means Balanced Steel Sword (+32% AC) gets a bonus of (32% * 30%) = 9.6% => 9%.
- +30% Block Chance to the BC bonus from that weapon (if any), rounded down.
- +10% Critical Skill to the Crit bonus from that weapon (if any), rounded down. So if your weapon has less than a +10 Crit bonus, this does exactly nothing for you (unless you level the skill up more). Dagger of the Shadow Priests would get a +2, a handful of +10 and +13 items (like Flagstone's Pride) would get a +1, and the rest get bupkes.
Affects: fighting with no weapon or shield equipped.
Effects: +20% Attack Chance, +5% Block Chance, and +2 Damage.
- An easy rule of thumb for the 30% bonuses is that the skill bonus goes up one point on "the 4s, the 7s, and the 10s" of your item's stat. So +13% is the same as +10% for these purposes (i.e., the bonus is +3 for both), and +19% is the same as 17% (i.e., +5).
- While the first (free) level of the Shield proficiency seems nice, spending another skill point on Lvl 2 seems silly when you could just level up Bark Skin for the same +1 DR bonus, and not have the wear-a-shield requirement.
- Note that additional bonuses from multiple skill levels in these proficiencies will get factored in before the impact to the player is rounded down. So Lvl 2 on a weapon that had a +5 Crit attribute would yield a +1 bonus, even when Lvl 1 yielded zilch.
edit: spoiler tag and disclaimer added to the top.