Breathing through the nostrils is extremely important in pranayama.
Each nostril is associated with what are known as nadis (channels) that have either a calming/cooling or energising/warming effect on the body.
The left nostril is associated with the Ida nadi and breathing through this nostril has a cool/calming effect. The right nostril is associated with the Pingala nadi and breathing through this nostril has an energising or warming effect.
By breathing through each nostril alternately, as is done in alternate nostril breathing, balance is brought to the body.