Because your nostrils split their workload. Throughout the day, they each take breaks in a process of alternating congestion and decongestion called the nasal cycle. At a given moment, if you're breathing through your nose, the lion’s share of the air is going in and out of one nostril, with a much smaller amount passing through the other. Every few hours, your autonomic nervous system, which takes care of your heart rate, digestion and other things you don’t consciously control, switches things up and your other nostril does all the heavy lifting for a little while. The opening and closing of the two passages is done by swelling and deflating erectile tissue - the same stuff that’s at work when your reproductive organs are aroused - up in your nose.
The nasal cycle is going on all the time, but when you’re sick and really congested, the extra mucous often makes the nostril that’s on break feel much more backed up.
There are at least two good reasons why nasal cycling happens.
One, it makes our sense of smell more complete. Different scent molecules degrade at different rates, and our scent receptors pick up on them accordingly. Some smells are easier to detect and process in a fast-moving airstream like the decongested nostril, while others are better detected in the slower airstream of the congested nostril. Nasal cycling also seems to keep the nose maintained for its function as an air filter and humidifier. The alternating congestion gives the mucous and cilia (the tiny hairs up in your nose) in each nostril a well-deserved break from the onslaught of air and prevents the insides of your nostrils from drying out, cracking and bleeding.
Source:
http://mentalfloss.com/article/30363/why-does-your-nose-get-stuffy-one-nostril-time