Let's say you're in an accident. A texting driver swerves out of his lane and into your car. The good news: everybody's OK, and the other driver's definitely at fault. But the bad news is that your car's not so lucky.
Seems pretty cut and dried: the other driver is on the hook for damage to your car, right? No problem...unless the other guy doesn't have insurance. Or doesn't have enough insurance.
If the other driver doesn't have auto insurance (most likely a crime itself!), your uninsured car accident coverage typically pays for the damages to your car - and also for injuries resulting from a covered loss. (Although in many states, this is covered under an insured's collision coverage).
If the other driver does have insurance, it's possible his coverage limits aren't high enough to cover the damage to your car. Or enough to cover injuries from the accident. That's where underinsured insurance kicks in, picking up the difference.
You probably also noticed that uninsured motorist and underinsured motorist coverage has bodily injury and property damage components. Bodily injury coverage typically pays covered medical expenses for you, your passengers, or family members who might be driving your car. Property damage coverage typically pays for damages to your car. (In many states, this is also included in your collision protection, so you may want to check your policy to confirm it.)