I think it was Mayfair Games who coined HTK or "Hits to Kill" instead of hit points, and that's probably a better way to look at it; how many solid blows you can take before going down.
D&D has always suffered from cursed design, as it's made two very different promises to people who want to play it- that it offers strategic, tactical battles and that it's a game for acting in and creating amazing stories.
Some parts of the game are thus very heavy on crunch and abstractions to allow things like "lone warrior in plate standing toe-to-toe with a 20' long dragon". Some parts of the game are flavorful and intended to evoke a feeling that you're playing a person living in a fantasy world, such as spell names being slightly more evocative than "fire attack" and "ice attack".
Never has D&D fully served one of it's two masters; the pendulum swings to and fro with each new iteration over the decades. So while "hit points" and "Armor Class" are abstractions to attempt to simulate a veteran warrior's ability to survive in combat, "cure x wounds" helps serve the narrative; obviously, clerics are calling upon their gods to heal wounded warriors!
Characters in D&D aren't actually wounded in combat until they fall down according to the mechanics...until it's decided that they need healing, and then they are. The narrative thus follows the mechanics.
That has always rubbed some people the wrong way, who think the mechanics should follow the narrative, as again, D&D makes this promise that it's a roleplaying game about interacting with amazing stories of adventure. The game is trying to be different things for different people at the same time, so it simply cannot be fully one or the other, and when it strays a bit too far in one direction, the fanbase splits in half as a consequence.