Your nose and respiratory system warm the air to body temperature, protecting the sensitive lining of the lungs and bronchial tubes. Most people breathe through their nose when they can. When your nose is blocked, you have to switch to breathing through your mouth. This is because the nose humidifies the air you breathe, keeping your throat from getting too dry. Sometimes people snore because they are unable to breathe through their nose.
Newborns breathe exclusively through their noses.
This becomes important during eating, when the mouth is full. Thus, anything that blocks the nose in a newborn will lead to the inability to breathe during eating, and so must be attended to promptly. Your nose also keeps diseases out of your body. The other important function of the nose is smell. While humans have a less developed sense of smell than some other animals, our ability to smell still accounts for important responses, such as appetite and emotion.