I will quote snippets from the Player's Handbook here. If any of them are too much, tell me, and I'll trim them. :) The post goes into a digression on what damage means with regards to killing a creature, but as a summation to get to the main point.
Hit points are described in the rules on page 136 of the Player's Handbook as "...how much punishment you can take..." While you can certainly play this way, I find the description of hit point loss given on page 145 of the Player's Handbook more compelling:
"[hit points] mean two things in the game world... ability to take physical punishment... ability to turn a serious blow into a less serious one. ...divine favour or inner power ...[independent] of hit points, a dagger through the eye is a dagger through the eye. ...Damage gives you scars...[damages] your armour...gets blood on your tunic."
Further, you have basically four possible states of health: Fine, disabled, dying, and dead, and you're fine until 0 hit points. Massive damage is also not an optional rule, and the 50-point threshold suggests that there's an upper limit to how much damage you can take and still call yourself "mortal" - ie., with a high enough Fortitude save. For example, "Yes, that is just an armour dent, but it's a four-inch deep armour dent. How are you still alive?"
Going to the suggested section on helpless defenders on page 153 of the Player's Handbook, we find: "...bound, sleeping, paralyzed, unconscious...at your mercy." A critical hit is automatic, and the target also dies on a failed fortitude save of DC 10 + damage dealt.
Let's assume a reasonably-competent sword-and-board fighter - Not an optimized build in the rules, but it'll prove the point. At level 1, with a +2 strength bonus and 1d8+2 damage, on a critical hit they do 2x1d8+2, or 13 damage.
With a DC 23 fortitude save or death, a creature needs a fortitude saving throw of +3 to save on a natural 20, which is a critical success in any case. To have a 50% chance of living, a creature would need a +13 fortitude saving throw, which is well into the point the character has transcended ordinary mortal limits - Which is any character above character level 6. Reference:
So, what does it mean when you have a positive hit point total? You've taken superficial or "surface" damage; your armour is dented or has missing scales or chain links; the divine favour given to you by your deity, which normally causes events to favour you, has waned; you've got a bloody nose and/or a scratched torso...
But you haven't taken any "real" damage. None of your wounds are bleeding freely. You don't have any broken bones, or even bruised ribs (that'd be disabled). If you have bruises, they aren't enough to impair you. You aren't missing any limbs. I would argue that "missing a limb" is one of the things that happens no earlier than -1 hit points, and should perhaps be reserved for -10 or lower hit points.
So, if you're wondering how to triage a village, or what damage means, anyone of 0 hit points is stable as long as they don't move - Think broken ribs or bones; spinal damage; bruised organs; concussion - things that could kill them if they move. Which brings us to dying. This is anyone bleeding from a major wound, internal or external. I emphasis bleeding here, as it's a very plausible explanation for many creatures for why they're losing 1 hp/round. They should be treated first. Dead is, of course, dead, and the power to raise the dead is costly, won't always be accepted, and needs to be measured in very deliberate triage.
Anyone of positive hit points is more-or-less fine, and is probably either at the tavern getting drunk and boasting, or at the local church praying and waiting.