Hit Points

How much health do I have left?
No aspect of white box or D&D in general has caused me more trouble than hit points. What do they represent? Why does a character ignore the effects of being hit right up to the point of going unconscious? When does death occur for the PC? Many such questions have plagued me over the years and I am convinced that it is a sign of overthinking! When it comes right down to it, a hit point is just a game mechanic; an abstraction of a resource that can be worn down and exhausted. To a lessor extent, the abilities of Str, Dex, Int, etc are too, because they can be "drained" away magically. So knowing full-well I am at risk of overthinking hit points, I shall dive right in and discuss them at length, in game terms, of course.
Over the decades I have given a lot of thought to what a hit point represents. At times I have tried to convince myself of the truth of various theories. Obviously it represents in some way the physical body- the body of the PC- that can be damaged, wounded or killed. It is also more than just that, especially at higher levels when PCs have more hit points it really becomes a measure of how long they can stand in harms way and absorb attacks while continuing to function. It seems improbable that a 2-pount hit taken by a PC with say 36 hit points amounts to much of a wound. It's a scratch at best and maybe less. It chips away at the PCs ability to absorb damage from attacks, but in no other way affects the PCs ability.  Healing complicates things a bit because it can take days to naturally heal that 2-point "scratch". All to the good I say for trying to explain things that perhaps are best left unexplained.
I currently tend to think of hit points as hit points...nothing more. My days of searching for "realism" in games is mostly behind me at this point and self-explanations have lost their appeal.  I say mostly, because it's true...occasionally I slip back into my old ways of thinking. So simply put, hit points are a resource, explain it how you like, or don't. It makes no difference. When your PC has some you can take action and when your PC is out of hit points, PC death is immanent.
Narration in game is something different, however. As referee, I like to be descriptive about combat, etc. and I try to tell PCs how they have affected the baddies with a hit as well as how they have received damage. As a general rule, I like to say damage is occurring as some form of fatigue or insignificant injury until remaining hit points are around 6 or so, then I start to describe damage as real bleeding wounds. I say 6 HP because I currently favor all PCs rolling a d6 for hit points regardless of class and I like to start PCs off with max hit points. It makes sense to my twisted mind and seems to be working in actual play. BTW- I also like to invite the player to describe in their own words how they finish off the bad guy who reached zero HP.
I have come to this approach to hit points by traveling a long and often torturous path of reasoning,  borrowing from other sources and trial and error. For a while I used Con scores as "real" body points from which wounds are taken and treated hit points as fatigue (which returned after a good night's rest). This seemed logical to me at the time as it extended the life of PCs by giving them way more ability to absorb damage at low level and "explained" why higher level characters can absorb so much damage. Before trying out that mechanic I had treated the initial HP score as "body points" and all subsequently earned HP as something akin to fatigue points.
Finding a way of making low level characters less "squishy" in my game was a goal of mine for the longest time. It seems to be a morale killer for players to keep rolling up new characters. Then I stumbled on the idea of having them roll several PCs to start and use as many of them at a time as they liked. It's the way we started playing the game way-back-when before the days of one PC per player. White box has a nice feature of making the higher level PCs much less likely to be killed (unless the player puts them deliberately at risk) since they have those higher hit point totals and it is precisely the higher level PCs that players get attached to having started them out at 1st level and seen them succeed while their litter-mates die off.  The survivor(s) develop character through play and become a player's favorite(s). Multiple PCs per player also has the advantage that should a PC be lost at higher level, the player probably has another close to the same level with which to continue campaign play. Henchmen and hirelings are another way of "padding" the party so as to avoid catastrophic PC death. Favored henchmen or even a hireling with "character" can become the player's PC on short notice in the event of character death.
It's fun to think about game mechanics, what they represent and how to improve on them. That's part of the hobby, but it can also become a tyranny if we forget to remind ourselves, it is just a game. Not everything requires a good explanation. The fantasy adventure game, and white box in particular, seems particularly well suited to such rules analysis, discussion and experimentation. I believe the white box practically invites us to take the game beyond the rules as written. Just take my advice and don't overthink it.