What do they do?

Sometimes, I'll see a hit that says "Ignore Armor" (self-explanatory) or "Cleave" (not sure about that one) or that seems to do a bucketload of damage.

Are those Critical Hits?

If some, anyone has some clarification on the game mechanics behind them?

I ask, because I'm wondering how worth it Weapon Master is...

This question never answered?

I can answer it!

Critical hits are random, awesome to deal, and annoying to recieve (I lost a Super-Elite Minotaur King to one, and I have lost count of how many Ironman-mode heroes died in one shot :(

All critical hits deal a bucketload of damage. However, depending on the damage type, they have other effects:
Piercing Weapons ignore armor on a critical hit - In addition to dealing a bucketload of raw damage, they also ignore the damage reduction armor usually grants. Since most units (especially high level ones) draw most of their staying power from Armor more than hit-points, this is always significant.

Slashing weapons Cleave on a critical hit: All adjacent enemy armies are hit, with the main target taking critical damage. It tends to turn large groups of Tier 1 infantry and archers into colorful battlefield carpeting

Bludgeon Critical Hits stun the target, reducing the affected unit's attack speed, combat, and damage. It may be possible it reduces damage by just reducing combat (Turning normal hits into glancing hits, and reducing the target's own chance of scoring a critical)

Ice critical hits freeze the target, slowing them to a crawl and turning them a nice shade of blue.

Fire critical hits ignite the target, causing damage over time and forcing the unit to constantly move.

I'm not sure what the effects of Lightning or Magic are on critical hits, if they even can crit.

Criticals are not random they are determined by a "%" ... You died in one shoot due a "Death Blow" not acritical.
"Death blows" deal 4 Times the damage as opposed to criticals that do only 2 times the damage ... you can say that "Death Blow" is a Critical Critical hit >: ) You must be talking about "Crushing" type of damage ... and as far as I know it just reduces combat statistic to 1 (speculation). Lightning criticals drain the targets mana ... I don't have any clue what magic cricals do since Magic damage is kinda rare.