Could you explain please? I've never seen a copy of HQ and associate the name with a Descent style boardgame.
[MENTION=57948]triqui[/MENTION] gave a decent summary - PCs are lists of freeform descriptors with numbers next to them, action resolution is descriptor vs descriptor, and the benefits of broad vs narrow descriptors are regulated by the GM applying appropriate penalties to those broad descriptors that might overshadow more narrow descriptors on other players' PCs.
To elaborate on action resolution: it is d20 roll under, with results therefore being success, critical success, failure or critical failure. (Think RuneQuest, but with d20 rather than d%.) The "success level" of the two opponents are compared to get the overall result. As triqui said, a bonus of 21 is actually a bonus of 1m1, which means it's like a bonus of 1 (ie hard to roll under) except the mastery gives you an automatic "bump" of one "success level". (There are also Hero Points that can be spent to bump. And obviously if both opponents have masteries and/or spend Hero Points then the bumps can cancel one another out.)
There is a robust augment mechanic, and some descriptors serve mainly as augments (eg if you have the descriptor "Shining Armour 12", you are unlikely to actually use that very often in a check, but you can use it to augment other abilities - say your Knight 17 ability, if you find yourself in a joust). Relationships are often used as augments too: so my Love for Roslyn 14 might be used to augment my Knight ability in that joust if the agreed stakes of the joust are that the Black Knight will free the lovely Roslyn if I can unhorse him in 3 tilts at the list.
The opposed checks can be either simple contests - a single opposed check to determine success - or complex contests - a system not unlike skill challenges, though because there is active opposition it's about racking up a certain number of successes before the opponents, rather than about successes before failures. (I think this system is in fact one obvious inspiration for skill challenges.)
It is the same action resolution system for all conflicts - combat, non-combat, etc - with the appropriate abilities determined simply by the applicability of the descriptors.
What I've described above is found in HeroWars (the original version, set in Glorantha with a lot of example descriptors with strong Glorantha flavour) and HeroQuest first ed (a revision of HeroWars, still set in Glorantha). HeroQuest revised is presented as a generic narrativist adventure RPG. It's two main innovations on the earlier versions are (i) changing the way that successes are tallied for complex conflicts, and (ii) introducing the Pass/Fail cycle for setting the target numbers on the GM's side of conflict resolution. (These aren't strictly DCs - they are used for resolving the GM's die roll in conflict resolution.)
The basic idea of the Pass/Fail cycle is as set out in the 4e DMG 2 (Robin Laws has basically cut and pasted that discussion out of his HeroQuest revised rulebook). It factors into target number setting in a very simple way: every time the PCs succeed at a conflict, the target number for the next one goes up (there is a simple chart in the rulebook that scales these numbers relative to the PCs' own numbers), until eventually the PCs fail in a conflict, and then the target number goes back down. So the idea is that the desirable pacing of a pass/fail tension/release cycle will occur without anyone having to do anything except follow the target number rules and then roll the dice.
Because the idea that the PCs will (eventually) fail is built into this system, it has a lot of good advice on how to narrate failure as something other than a dead end (although I think the advice in Burning Wheel is even better).
It's interesting to note that this is actually the opposite of some 4e skill challenge advice, which says if the PCs fail the skill challenge make the next encounter
harder. I think Robin Laws approach might be better - successes should rack up the tension, and failure should be followed by success rather than more failure, I think. I don't think I'm fully consistent with either approach in my own GMing practice.
Some other interesting features of HeroWars/Quest relevant to 4e are (i) that all meaningful advancement is in the fiction, not the mechanics; (ii) that the
stakes are purely fictional, too, as the actual action resolution mechanics are so simple and non-tactical (complex contests have some bells and whistles that allow a bit of tactics, but nowhere near the scale of 4e combat); (iii) that the GMs target numbers for the opposing checks in a conflict are set on a purely metagame basis (like the DC by level chart) which means that narration of opposition must be adapted to fit those numbers, rather than vice versa - a lot like a 4e skill challenge, in my view (and in my view this is also non-coincidental - I think it's pretty obvious that 4e skill challenges and DC rules were modelled in part on HeroWars/Quest-style complex conflict mechanics).
HW/Q is also one of the RPGs that I often bring to mind as a counterexample to claims like an RPG
must have distinctive (and detailed) rules for combat compared to non-combat, or
must have action resolution based on stat+skill, or
must aspire to its mechanics being a "physics enging" of the gameworld.
That's probably a longer answer than you needed!, but might give you an idea of what I meant, and also why I see 4e as the most indie-ish version of D&D.