If I am running a fight between a giant and a group of players, when I describe damage, I don't say, "The giant scared the poop out of you with his club for 17 points of damage, you're going to need new underwears." I say, "The giant knocked your liver out of your body for 17 points of damage, you're going to need to stop at the convenience store and get another one."
If I was to be excruciatingly honest, I would normally say, "The giant hits. You take 17 hit points of damage."
However, on the infrequent occasions that I did want to add a bit more description, I would say something along the lines of, "The giant deals you a glancing blow with his club" (if the PC still had quite a few hp left) or "The giant's club catches you in your side. You think you might have cracked a rib" (if the PC was quite low on hp afterwards). As long as the PC was high on hp, arrows "graze", swords and stingers "nick", "cut" or "scratch", blunt weapons leave "bruises". If the PC was low on hp, I might describe something more serious, e.g. a deep wound in a non-vital part or cracked bones, but again, nothing life-threatening or that could significantly impact the PC's ability to make attack rolls without penalty. It's only when the PC dropped to 0 hp or less that I actually described life-threatening wounds, but again, nothing that a PC could not recover from completely in time (no decapitatons or loss of limbs).
I guess I had gotten into the habit of describing hit point loss in this manner even before 4e because because hit points have always been presented to me as more than physical - a high-level fighter low on hit points would be covered in nicks and scratches, but the sum total of all those nicks and scratches wouldn't even be enough to cause an actual hit point worth of damage. A normal man, or even a frail and weak man with 1 hp, covered in those same nicks and scratches wouldn't be dead, or even significantly hindered. So, while there was always a physical component to hit point loss, it was miniscule.
So, fast forward to 4e. What changed for me?
1. Hit point loss can be entirely non-physical. Magic can frighten a man to death, depress him to death or insult him to death. Fine. I can deal with that. It's magic. If a magic ray of green light can kill a man even though he is completely fine physically, I can accept that magically-induced fear, depression and anger can also kill.
2. Hit points can be restored more easily through non-magical means. Not an issue for me since I've never gotten into the habit of describing gory wounds. I just pile on the nicks, scratches and bruises.
3. A character can drop below 0 hp, be in danger of death, and recover back to full hit points within 5 minutes by non-magical means. This part is more tricky, but fortunately, I've never gotten into the habit of describing dropping below 0 hp as anything that could cause permanent impairment. What I have to be careful about now (when there is no magic healer in the party) is to ensure I don't describe dropping below 0 hp as anything that could cause temporary impairment, either - no broken bones, for example. These days, on the occasions when it happens, my preference is for profuse bleeding. It's possible that a character could die from it, but it's also plausible (at least to me) that once the wound is bandaged up and the blood loss is stemmed, a character could ignore the pain and press on.
