In a study reported in the American Journal of Respiratory and Critical Care Medicine (2002; 166: 144-145),researchers at the Karolinska Hospital in Stockholm, Sweden found that nitric oxide levels in the sinuses were 15 times higher during humming than during normal, quiet exhalations. Nitric oxide (NO) helps to dilate the capillary beds and increase blood flow. Humming had the effect of dramatically increasing the gas exchange in the nasal sinuses. If fact, during normal exhalation the gas exchange between the nasal passages and the sinuses was about 4 percent. When the volunteers (all "healthy") hummed, the gas increase increased to about 98 percent.

Humming also holds in more oxygen as you exhale making each breath more efficient in terms of blood oxygenation.  It helps extend the exhale which often slows the breathing down allowing for more oxygen to be extracted from the air we breathe thus decreasing the oxygen cost of breathing. 

You may  have noticed that people who often hum seem relaxed and at peace.  Humming also tends to utilize the "larger" part of the breath that I associate with the Bel Canto aspect of classical voice. 

Humming also helps the sinus cavities.  For sinus troubles SinuCleanse may be considerably more effective. 

Hum more - live longer.  Rapid Breathing-Development