"Quiet inspiration" is the intake of air into the lungs via the contraction of the diaphragm and external intercostal muscles only, while "quiet expiration" is output of air from the lungs by relaxing these same muscles. They stand in contrast to forced inspiration and expiration. In forced inspiration, extra accessory muscles are used to take in air faster, while in forced expiration abdominal and other muscles force air out faster.
Quiet inspiration and expiration are the normal methods humans use to breathe when relaxed and unstressed. During this process, only inspiration is an active process, largely of contracting diaphragm muscles to cause the diaphragm to lower, decreasing the pressure in the lungs. This causes the air under normal atmospheric pressure outside to rush in, carrying the oxygen needed for survival. Quiet expiration, by contrast, is purely passive, a simple relaxation of the muscles that causes the chest cavity to expand, returning it to its original volume and forcing the inhaled air out.
Forced breathing often happens during physical exertion, where gas must be exchanged faster and more thoroughly than in quiet breathing. Normal quiet breathing exchanges less than half the air in the lungs, and quiet inspiration does not fill the lungs to their full capacity, according to McGraw Hill Education.