There is a lot of focus on breathing in yoga. One reason is that calm, deep breathing sends an immediate signal to the brain that everything is calm; there is no threat, nothing to worry about. It is difficult to do calm and deep breaths if you stand in front of something threatening or you feel stressed and anxious. 
When you breathe calm, deep breaths the parasympathetic part (rest and digest part) of our autonomic nervous system is activated. It will give a better balance towards the sympathetic part (fight and flight) that is activated when we respond to a threat or stress.  

Should I breathe through the nose or the mouth?
When you breathe through your nose you will breathe in air that is warm and filtered. The air will also pass by the sinuses where you have nitric oxide that among other effects strengthens your immune system. 
There are some breathing exercises in yoga where you breathe in through your mouth. These exercises will give a calming and cooling effect.
The normal breathing in yoga is however to breathe in and out through your nose. 

Do you want to try some calm, deep breathing? Join one of my online classes, or try deep balancing breathing on your own. You find the class at Do yoga on your own.