There are 2 ways to breathe, chest and diaphragm. Breathing with your diaphragm is actually healthier, and your rib cage doesn't move. Instead your stomach goes out when you inhale and in when you exhale. Breathing with your chest, your ribs go out when you inhale and in when you exhale.
The diaphragm contracts, causing air to fill the lungs. As the lungs expand, the ribs very slightly expand upward and outward, but overall there is only slight basic change to the skeletal structure. Breathing is an active process - requiring the contraction of skeletal muscles. The primary muscles of respiration include the external intercostal muscles (located between the ribs) and the diaphragm (a sheet of muscle located between the thoracic & abdominal cavities). The external intercostals plus the diaphragm contract to bring about inspiration: Contraction of external intercostal muscles > elevation of ribs & sternum > increased front- to-back dimension of thoracic cavity > lowers air pressure in lungs > air moves into lungs Contraction of diaphragm > diaphragm moves downward > increases vertical dimension of thoracic cavity > lowers air pressure in lungs > air moves into lungs. Source: http://people.eku.edu/ritchisong/301notes6.htm