Carnage applies to all "on-hit" effects of weapons: Wounding, Disorienting, DR Bypass, Draining, Overbearing, Stunning, Convert Graze to Hit, et cetera. for the on-crit effects, i believe the Carnage attack has to crit, not the parent attack.
it's a wildly powerful skill.
as for proc, it depends on who you talk to or where you are reading as to its etymology. some say its shorthand for Programmed Random OCurrence (eg, x has a y% chance to activate z's effect). others will tell you its short for procedure. with relation to gaming, it's just a synonym for trigger, activate, et cetera.
This makes sense, since it's not uncommon for words, slang or otherwise, to have unknown origins and multiple theories as to those origins.
I prefer "trigger" myself, though. It seems much more accurate and descriptive.
Looking at the list of effects that Carnage might be able to apply, there are some good ones there. But I'm tempted to think that Draining could be among the best simply because Barbarians (from my understanding of the class) tend to take a fair amount of damage, and a carnage AoE drain on multiple enemies could heal a LOT of END in a short time! Particularly since it's not an on-crit only effect.
it works wonderfully. Barbarian can stack good DR with Thick Skinned and Crucible Knight affiliation (if PC) for decent tanking. Retaliation also works with Carnage, so Fire Godlike for more DR + Retaliate + Coat of Ill Payment (not sure if Retaliation stacks). and to top it off, Tidefall has Draining and Wounding for Carnage shenanigans. this on top of the (questionable) Jolting Touch interaction makes Barbarian probably the best DPS class in the game. still not as good as Wiz or Druid cause no CC but pure damage wise, it's hard to argue.
it's why i prefer Weapon Focus: Soldier. Tidefall is incredibly powerful and you can swap in Pike (Tall Grass) for Barbarian.