hit points are not about health

Hit points are about energy and ability you have to fight.
If you fell from a height, you are in pain, you fight worse, but it is passing, your HP go up.
Food do increase HP, as it recover your strenghts <--- here answere to your post Natrina
HP are even about illness, being Ill you won't fight good and so you have less strenghts, so your HP reach zero faster, coz there are less of them. But to restore the level of HP to their normal, you need to stop being ill, what isn't so easy as with overcoming pain after a while. It should take time. At least it's how i imagine it.
Think of HP as health makes no sense. How do your wond recover in real? Days or months (whoever trying to comment, keep in mind PS day is shorter, but your char doesnt live faster, there is no argument for that). In PS the HP bar is rising fast. There is no Health bar, if there were, it would probably keep the hp bar decreased until you recover (see lenght of recovering in real life)
The potion of healing is increasing HP bar, but it doesnt heal you, but recover your strenghts, what explain how it is possible, it works so fast.