Fish breathing is medical slang for a sign of acute respiratory distress when a person gulps in air through his mouth in an attempt to breathe. It's so called because the opening and closing of the mouth resembles a fish periodically sucking in water. It usually means that something in the respiratory tract or the heart has gone horribly wrong (i.e. gunshot wound, multiple organ failure, pneumonia).
"The patient was fish breathing when we found him, he turned out to have a GSW to the left chest with hemothorax. We drained out all the blood and sewed him back up but the injury went septic and he died the following morning."
by Woolie Wool July 19, 2013