They're simple. They measure how much damage or injury a target can sustain before it dies or is destroyed. In and of itself, they're fine.
The issues arise when Hit Points get yoked to other systems or mechanics. The association between the clear and obvious purpose of the concept with the subjects of its employment--that Hit Points measure how much you can take before you die--gets messed up when you then latch on concepts such as Experience Levels and link the two. (Increasing Hit Points with level, a Dungeons & Dragons staple, being the most obvious example.)
I am dissatisfied with anything other than strict association. The reason is due to increased knowledge of how injury/damage and healing work, as contrasted with the abstractions employed to make manageable at the table that same issue.
I've been around a long time, so I'm aware of the alternatives. I'm going to stick with what I find to be a better compromise.
- TORG: TORG uses a comparison of Effect Value vs. Toughness, read through a table, to determine a Wound/Damage result. Three levels incapacitates, and four kills/destroys. As this was a West End game, the similarity with the d6 System as seen in its version of the Star Wars Role-Playing Game is notable- and desirable.
- Traveller: The classic form has a very playable abstraction of the importance of injury. Damage is directly applied to physical stats, with incapacitation when one goes to zero, severe injury at two, and death at three. Fantastic system, as easy as the D&D default regime, and avoids all sorts of issues.
- Basic Role-Play: Static Hit Point scores, rarely modified after character creation, and largely determined by physical size and stature. Playable, sensible, and (as with Traveller and TORG) proven to work as intended.
(Note: This post was intended to go up on this date, but an unforseen access outage delayed it to the 3rd of November, 2015.)