Why does after running, a person would appear out of breath and increasing breathe rate? what is the mechanism involve?

Anaerobic metabolism: Push the body's need for oxygen beyond the oxygen supply, and glucose will be burned to Lactic Acid which then accumulates. The Lactic Acid lower ph so a person compensates by breathing more rapidly to remove carbon dioxide. This is subtle; it also helps the person get a bit more oxygen overall but the deep breathing in athletes is mostly about getting rid of carbon dioxide.