This sounds fairly self-explanatory, and it is, to an extent. This will step in and give you coverage when the other party either does not have insurance, hit you and ran away, or does not have enough insurance to cover the damages.
Unfortunately, the most common usage of this coverage is for hit-and-run accidents. If your car is parked, and someone sideswipes it, or you are rear-ended and the other party leaves the scene (this one has actually happened to me, personally and it is not fun); these are all instances where you would need to file a claim under your uninsured/underinsured motorist coverage (also known as UM/UIM).
However, there are other instances where UM/UIM would come into play. If, for instance, you are in an accident with another person and that person does not have insurance at all (or it has lapsed), you would need to file any claims on your own policy to get any reimbursement or payment from the company. There is a deductible, so that completely stinks (considering if they had insurance, there would be no deductible on your part to pay), but at least you do not have to pay the full amount of the damages.
Another instance where UM/UIM would be used is if the extent of the damages caused by the other party to you or your vehicle exceeds the limit of their insurance. Say there were multiple vehicles involved in the accident, there is only so much an insurance company can pay out on a single claim. Unfortunately, you might not get enough (or any) of the payout to take care of your damages. In this case, you would need to file a claim on your UM/UIM coverage.
Uninsured/underinsured motorist coverage is voluntary, but if you decide not to take it (against the advice of your agent), you do have to sign a form to confirm that you understand the potential consequences and are willing to accept them. As an agency, we will never recommend you reject this coverage, because the unexpected can and will happen!
If you would like further information on this coverage, please reach out to our agency.