Nogare is karate’s “soft” breathing method. Some karateka call nogare "combat breathing," because it conceals your breathing motion, and preventing opponents from timing their attacks to contact while you are inhaling. In practice, fighting mostly consists of short ibuki breaths, but nogare breathing should be used in lulls or breaks in the action to calm your nerves and help prevent fatigue.
Nogare is much like normal breathing, with a quick, silent, and deep nasal inhalation, and a gradual silent exhalation through the mouth. The abdominal muscles are slightly tensed to hide the rise-and-fall of your chest, which telegraphs your breathing.
Nogare breathing prevents fatigue by encouraging air absorption. A fatigued person's “huffing and puffing” comes from a craving for more oxygen; but this craving causes people to illogically push the air out of the lungs before it can be fully absorbed. Slowing the breathing rate allows the oxygen to soak into the lungs, and you can draw more benefit from each breath.
Nogare breathing also has a calming effect, which is essential because adrenaline bursts can cause unwanted tension and a degradation of fine motor skills, which can prove to be a liability.