I think Tuft has it backwards. The fireball, and lots of attacks, do actual damage - but so long as you have hit points you can stay on your feet and keep fighting. Likewise, someone healed by martial healing is a lot like Die Hard's John McClane -- physically beat to crap but still able to beat down a whole lot of enemies. The only thing that hit points measure is how long you can stay in the fight, not how much damage your body has already taken.
That's how subdue works. Maybe they're hanging on to the brink of unconsciousness, or maybe they're just completely demoralized, but your final blow puts them over the edge into uselessness.
In this regard it's very different from earlier editions, and my analogy isn't perfect. Like any hit point discussion, your brain sort of hurts if you think about it too hard. Still, it works for my own suspension of disbelief.