Really it is easier gamewise to consider this in terms of actual trauma to the body. If you're at 3:00 you've only been bruised/scratched a bit, if you've been healed to this point, your wounds are mostly closed up and beyond being sore you're fine.. Not dangerous. 6:00 its looks a bit more serious, you've got a black eye and had you limp yourself away from that bar fight, but you're alive, and if push came to shove you could still operate your motor functions like running, putting aside the pain.
9:00 and beyond are gradually more serious injuries, but the thing is you're dying. Satibilized means, is this wound KILLING you right now. That's as simple as it gets. Have you been stabbed in the stomache with a knife? Shot somewhere that wasnt through and through? Fallen and cracked bones, ribs, or other shit that cause internal bleeding, got a Major concussion? Was one of those cuts seriously filthy and the infection is going to come back to bite them?
The oClocks are a way to Hit Point combat, meh. Give the wound a name, let them know what hurts and why. When they're no longer in danger from dying they're stable. Mechanically this means they've been treated by someone that can help them, cause knowledge of how to help isnt just day to day or googleable. If they got shot, they're stable when they have had the bullet out, the wounds stiched and are lying on some makeshift bed for few weeks while they recover at superhuman speed. A broken limb? Stable when its all tied up clean and casted, so their bones are locked together right and the wounds clean so they dont got to cut nothing off later.
Stablized. It is no longer killing you. Give your wounds a name, and they, the wounds basically tell you this for you.