I run the game with certain assumptions, but the main one is that during combat you are constantly look for openings to exploit, even if the game mechanics say you're only making a single attack. The stuff that actually gets rolled for simply represent the most important attacks your character commits to. Otherwise, there's a constant duck-and-weave to combat not unlike two boxers who make several probing shots before going all in.
Next up is to understand that HP do not represent how much actual damage you can take, but instead represent your character's ability to turn otherwise fatal hits into glancing blows. I mean, let's face it: a single sword stab is generally enough to drop a man right there. At best, he might pose a risk while bleeding out, but he's more likely going to writhe around screaming in pain until someone sticks him with a spear moves on. But with D&D, your character can learn to roll with the hits or position himself at the last second to take it in a non-vital location, etc.. That ability/skill/luck/etc is what HP really is.
So how do you narrate it? It can vary a bit, but I generally like to identify a point where the damage is no longer superficial, meaning the next one or two hits could very well drop the character. Some DM's assign a static value, like 10 HP, and anything that goes below that is "real" damage. Others might do percentages of total HP. I personally set the value at roughly the amount of damage the biggest attack can deal, so if there's an Ogre that can hit for a steady 16 damage, then that's about where threshold is for that battle. If the Ogre hits a full health fighter (38 HP) with 16 points of damage, I know that the next such hit could be back news and can use that to better narrate the attack:
"The savage smashes you in the side with its great club -- you hear your shield splinter as it absorbs the blow, but you're not sure if you can take another such attack."
That's how I'd describe most actual combat hits that deal damage. If the Ogre just missed, narration is easier because I just describe how the beast wildly swings its great club into the table next to you, shattering it into pieces.
Anyway, it's also very easy to simply fall into the "the Ogre hits you for 16 damage, who's next?" mentality. But that's when HP makes the least sense.