Imagine that you own a $50,000 vehicle. You're driving along, minding your own business, and another driver comes out of nowhere and crashes into you. You're ok physically, but the accident has completely destroyed your vehicle. The other driver has liability insurance, but his limit (the maximum his insurer will pay) for Liability - Property Damage is only $25,000.
Uninsured / Underinsured Motorist insurance covers another driver's liability in the event that driver a) doesn't have any insurance, b) doesn't have enough insurance to cover the damage he caused, c) leaves the scene of the accident and is unable to be tracked down (hit-and-run).