Is that temp, perm, or healing? A one-shot heal for 1 point could save me from dying. A temp HP is not much- maybe something at first level, but why not give 5. A permanent HP is cool, but only means that I rolled one more last level. If this can happen 10 times a campaign, then you have something.
At some point during the night, the Inquisitor from Red Dwarf erased my character from history, replacing him with a parallel version who took slightly better care of himself. Nobody remembers this because the timeline has been completely overwritten.
With a fresh, new hit point, my character probably fell under the eyes of the Fates (even if their gazes didn't linger), and he's standing up a bit straighter.
Picture it: you're at the gaming table, playing a character. Someone at the table has used a rule that gives your character one additional hit point.
How has your character changed? What's different?
D&D (4E and PF2): "Not that anyone will notice, but I'm very slightly better at avoiding serious injury" Call of Cthulhu: "Hey I have slightly less chance of being taken down by a shotgun at medium range. Up close, still toast"
Games without hit points, but with vaguely similar mechanics:
Fate Core: "I have an extra stress box! I am now a serious bad-ass!" Savage Worlds: "I'll still be almost completely ineffective when heavily wounded, but at least I'll take longer to die!"
Games that do not use such concepts:
Agon: Heroes do not fiddle with numbers! They dare all and succeed, or fail and the gods weep for them!