One of the many ancillary services that the United States Postal Service
Quite simply, it is exactly as suggested - for a fee, your article of mail is insured against loss, rifling, or damage. It's generally a good thing to use when sending any article of any intrinsic value over mail, and the extra fees (see below) are a good thing to pay. It's also a little more encouragement for the mailman to take a bit of extra care while bringing your article from Point A to Point B, because after all, the government doesn't want to have to pay up.
Note though that, while this gives them a reason to take care of your article, it's only about as secure as the rest of the mail (which, all things considered, is fairly secure), and you can only insure for up to $5000 of value of the actual article, less depreciation - if you need a higher value, that's what registered mail is for. They also don't pay out on sentimental value or the time or money spent dealing with the loss - after all, it's a policy out on the mailed article, not on your time, and you can't feasibly place a value on sentiments.
Cost on this service is variable. Initial fee for $.01 to $50 is $1.30, $50.01-$100 is $2.20, and each increment of $100 or fraction thereafter is another $1. (You would get better value after a fashion by going with registered mail.) Return receipt and restricted delivery are available for articles insured for over $50 for the according fees.