An underinflated tire deflects more than one that's properly inflated. This increases rolling resistance, which increases wear at the tread surface as well as fuel consumption. There's a direct correlation between how much a tire is underinflated and how much faster it wears. As a rule of thumb, tire life will decrease 10 percent for every 10 percent it is underinflated. There's also a safety factor to consider.
Underinflated tires run hot because of excessive flexing.
The added heat can damage the tire and cause a blowout. An underinflated tire can cause other problems as well. The amount of air in each tire affects weight distribution between the wheels. An underinflated tire in a dual position doesn't carry its full share of the load. This in turn, affects chassis loading, traction, steering, alignment and braking.