What isn't often remarked upon is that, because hit points are abstract, they're not really necessarily tied to health. This makes them actually fairly powerful tools for packaging information about an otherwise faceless character. Let's explain by taking three model fighters, Bill, Ben and Ted.
Bill is a 1st level fighting man with 18 STR and 1 hp. He is extremely healthy and robust, but also absurdly reckless and belligerent; in any fight he leaves himself highly vulnerable to attack through his sheer uncontrolled desire to crush his enemy. A clever opponent need only wait for an opening to deal a killing blow.
Ben is a 1st level fighting man with 18 STR and 1 hp. As a child, Ben was cursed by his father's witch lover, out of spite for his mother. Ever since, he has gone through life with a bleak fate hanging over him: he will meet an ignominous end. He does not know how or where or why, but only that some otherwise humdrum accident or mistake will bring about his death.
Ted is a 1st level fighting man with 18 STR and 1 hp. Ted was constructed by a mad archmage when a teenager, who removed every bone in his body and replaced them with glass. Ted possesses vast strength, but his skeleton is so brittle that one decent blow is enough to shatter it irrevocably.
The otherwise uninteresting and uninspiring stat, in other words, can be interpreted into something unique - because of D&D's unintentional genius for the abstract.