Death Spiral is the internet RPG shorthand for any mechanic which uses life-status point (HP/Constitution/Life Points/etc.) thresholds to add penalties. The implication of the name is that once you start getting damaged, it becomes harder and harder to break out of the spiral, which ends in character death. At each threshold of the Death Spiral, the character's penalties for doing anything become more and more severe, to the point that any action becomes essentially futile. The goal then would, by implication, be to be the first to deal damage and lock your opponent into a death spiral while avoiding this yourself.
Contrast this to the Shop 'Til You Drop mechanic used in many RPGs. The character suffers no impairment no matter how low the life-status points drop until the character dies. This has no death spiral, but is essentially bizarrely unreal, unless Life-status points are thought of as not cuts and bruises, but abraded luck and accumulated fatigue. This goes against the convention of calling a success in combat a "hit" - a hit should mean you hit the opponent. Anything else is counter-intuitive. Perhaps using a different word - "success" or "threat" or something like that - would make it more acceptable as a model. With this change in approach, the Shop 'Til You Drop model becomes much a more reasonable abstraction.
There's also a variant on this - Shop 'Til You Fall Over. Sometimes a small negative life-status threshold is added below the zero threshold - if you hit this point, you are unconscious, with various penalties - possibly bleeding out, possibly comatose, etc.
Another mechanic used in RPGs is Buy Now, Pay Later, where the character suffers no impairment from wounds until combat is over, whereupon the bill becomes due. This is an interesting compromise between the Death Spiral and Shop 'Til You Drop. The penalties of a Death Spiral still acrue, but payment is postponed until pressing business is finished and the adrenaline wears away.
My games use another variant of the Death Spiral, which I call a Life Spiral. In this variant, your different thresholds of Life-status points trip differing conditions, not further penalties. In my games, the first threshold incurs a condition - Hindered - in which a small penalty is assessed to all actions. The second threshold incurs a different condition - Stunned or Unconcious - in which the character must make an appropriate skill or stat check in order to continue fighting. Otherwise, the character becomes disoriented and is out of action until roused by another. the third threshold - Seriously Wounded or Critical - incurs another condition in which the character falls over, cannot be roused, and begins slipping away unless tended to by another. The second threshold is a warning. You can continue, but things are getting dangerous. The third threshold is a limit. You cannot continue any further, and you may lose it all. These separate conditions serve to keep characters alive at the expense of dropping them out of combat.
Why is this a Life Spiral? Here's something anyone who ever ran an RPG knows - The Party Will Never Surrender! The only way to defeat a party is to kill them all. Consequently, the corollary to the party never surrendering is that Defeat == Death. The GM plays the opposition the way the party plays itself - the only surrender is death. Thing is, people survive losing combats all the time in real life. One side is almost never wiped out.
This brings me to The Importance of Being Stunned. Stunned characters are not responsible for surrendering. They can live without taint of cowardice or whatever it is that motivates the "never give up, never surrender!" zeitgeist which imbues PC parties. They can be captured, and they can maybe eventually escape and still win in the end. Defeat becomes temporary, not final. Since they can be captured, there's a reason for not wiping out the enemy when they are helpless - if you get a rep for killing prisoners, the enemy will do the same. If you want to live through a defeat to ultimately triumph, treat your prisoners decently.