The Pool is the central mechanic you use in managing your character in Heroes of Destiny. That's true of taking action. It's also true in taking damage. You don't have a damage track or hit points or anything else like that. Your Pool is your capacity to take damage as well as act. It ties all of that up into a single, tidy package.
Damage in this game doesn't have to be physical. It represents your ability to endure punishment and function in a situation, but this can be mitigating the effects of a retort in a debate as easily as it might be a punch to the face. Thus the damage rules apply to any kind of situation where one character is attempting to remove another from a situation.
You deal and receive damage in points, which are generated by effort like anything else. You create an effort pool to successfully strike someone, and you create a second effort pool to deal damage. You generate both in the same exchange, by the way; there's no spending for hit and then a separate spending for damage. It's a gamble to see how little you can spend on landing the blow so you can channel the rest into damage. Spend too little and the blow doesn't land, thus doing no damage. Overspend and you might hit reliably, but it'll be a fight of papercuts.
Apply damage to your Pool. As in generating effort, Hope and Destiny have different exchange rates, and here's where Hope finally starts catching up to Destiny. Each point of Destiny can absorb one point of damage. Hope, on the other hand, is all about what you dream of, what you're living for, and thus each point of Hope can absorb two points of damage. When you've got a lot of Hope, you can push on and keep going because you've still got so much waiting for you at home once this is all over, and nothing's going to keep you from it.
When a point from your Pool absorbs damage, it becomes bloodied. Bloodied points are useless. You can't spend them to generate effort, and you can't use them to absorb any more damage. They're done. Pull them aside as soon as you absorb the damage; you won't be using them again this exchange. If your entire Pool becomes bloodied, you're taken out. This might mean you're dead, unconscious, completely flustered and unable to continue debate, or anything else you and the GM agree is appropriate. The only hard rule here is that you're unable to act effectively anymore.