Nitrogen is less likely to migrate through tire rubber than is oxygen, which means that your tire pressures will remain more stable over the long term. Racers figured out pretty quickly that tires filled with nitrogen rather than air also exhibit less pressure change with temperature swings.
Passenger cars can benefit from the more stable pressures. But there's more: Humidity (water) is a Bad Thing to have inside a tire. Water, present as a vapor or even as a liquid in a tire, causes more of a pressure change with temperature swings than dry air does. It also promotes corrosion of the steel or aluminum rim.
Your tire pressures will remain more constant, saving you a bit in fuel and tire-maintenance costs.
Ask about out Nitrogen tire refill service.