In Dungeons & Dragons 5th Edition, hit points are nominally tied to physical damage—or symbolically tied might be more accurate. For example, let's say your 3rd level Warlock with 24 hit points takes seven points of damage. This does not mean the Warlock suddenly loses three pints of blood or three fingers. In this world's reality, which means in the fiction of the game, the result of that seven points of "damage" coming off the top of a fully rested 24-point high-Charisma Warlock might only be a bruised ego. But to that character, who has self-confidence through the roof, an unexpected seven point loss can be devastating. Losing seven hit points will shake the ego, morale, arrogance of many characters—especially if they depend on these to remain standing. There may be a little blood spilled, maybe a minor wound, but that is created in the fiction for a particular character, adversary, and combat encounter, and remains in the fiction. And right in line with this, a Barbarian with 42 HP will probably shrug off seven points of damage with a laugh. A little blood between enemies just makes a good story. In the fiction of the game, that seven point damage roll might also be a bruised ego, but to the Barbarian—with unshakable courage, the response could be to acknowledge the damage, nod appreciatively, and say, "Oh, so we're hitting each other now? Here, let me show you how to hit someone." Same seven points of damage, different response.
Since hit points (HP) do not correspond to physical damage in D&D 5e, with blood and scars or loss of fingers and ears, if you are tracking debilitating wounds and organ damage, or corruption and insanity in your game, then I think those should affect the character's actual stats, in the reduction of Strength, Intelligence, Charisma, etc. Your stats and associated ability modifiers represent your character's somewhat permanent capabilities—how much you know, how much force you can put into that axe swing.
Your character's hit points, on the other hand, represent courage, flexibility, luck, inner strength, and the ingrained fighting or evasion skills they can bring to bear to evade a killing blow. HP is a resource that can go up and down a thousand times in the course of a long campaign, which would be impossible if hit points simply represented your character's physical body, and loss of HP meant physical impairment, internal bleeding, infection, organ damage, bones broken or crushed. There wouldn't be anything left of your Warlock by the time they reached the 4th level. If they even make it that far. A character only has ten fingers (most humanoids anyway) and the loss of more than a few can permanently limit their ability to fight with many weapons.
HP is obviously tied to character death in the rules, but that final killing strike only comes after you've exhausted all hit points. Up to that point, even with a single hit point left, you're still in the game, with your full capabilities—your +6 Strength, Charisma, Wisdom, etc. This is also why a dragon can have hundreds of hit points. They are just that difficult to break, that difficult to bring to the point where they give up physically and mentally. A dragon reduced to zero hit points or lower might be "dead", but more importantly, their resolve has been broken, they are broken in spirit, or terror-stricken. This obviously goes for your player characters too, and that's why they are not beyond reviving in some cases. In the fiction, it's possible for your character to have zero hit points and not have a scratch on them.
Okay, that's basically it, there can be physical aspects of the hit point mechanic in 5e, but I think most of it is comprised of less tangible components, like fortitude, the confidence of years of training and combat experience, even arrogance. HP can represent just how badass you think you are, even if you're not as dextrous or charismatic in reality. How much of a high-level Bard's hit points is made up of unabashed pompousness? In some it's quite a bit—same goes for that dragon. And during combat it is your foe's fortitude and well of confidence after years of training you are eroding when your Sword of Uprightness lands skillfully and you do 21 points of damage. In the fiction of the game you may have only twisted past their defenses and given them a good scratch across the cheek, but the point is that it's so devastating a blow to the faith in their fighting abilities that their hit points just took a nose dive. Mechanically, you and your sword cut their hit points in half. In the fiction, you can see them step back from the fray, raise a hand to touch their cheek and come away with blood on their fingers—and then you see that sudden look of horror in their eyes when they realize this isn't going to end as easily as they thought it would.
That is what I'm measuring with hit points in D&D.
Note: this is also perfectly consistent with hit point recovery during short and long rests.