The fish goes through three stages

The first is when you see the fish quivering and shaking, as it tries to gasp some air. Then after a while the fish has no more energy to shake and so all it does is it tries to breathe. Then if you take the fish and throw it back in the water, then it will be able to still live and breathe.

But then there is the third stage. When all you see is the fish slowly moving it's lips, closing them up up and down. At that point if you took the fish and you threw it back in the water, it would still die because of the lack of oxygen. The fish has now experienced total organ failure. It will die anyway...