The nasopharynx- from the nostrils to the back of your throat- provide both moisturization and heat to the air you inspire, in addition to the filtration by nasal hair and other small hairlike projections (cilia). Colder, drier, unfiltered air can cause spasm of the small airways, limiting maximal air exchange between the atmosphere and the diffusion surface in the lung- the alveoli, where oxygen and carbon dioxide exchange.
Mouth breathing provides a larger portal for air entry in to the large airways (trachea), makinf the work of breathing during exercise easier.
When I first started running, I would really focus on breathing in the nose, and out the mouth. I found it helpful b/c it is almost like a mantra, keeping the mind from noticing how far I had left to go!
The breathing mechanics are better in overall, but it is very difficult when the body's conditioning has not caught up- i.e., the ability to utilize oxygen delivered in the lung.