Quiet title is an action by the court to resolve an outstanding issue affecting title.
Here's an example. Let's say we have a seller conveying two parcels of land, both of which have been in the family for years. Our seller, now elderly, has presumed that she was the sole owner of both parcels. Our title search reveals that both parcels were conveyed to her by her father fifty years ago, however, at the time of the conveyance, her father only owned 50% of the second parcel. The other 50% had been owned by his cousin.
It's the job of the seller to clear title to the 2nd parcel and to do that, she will have to find the heirs of her 2nd cousin. If they cannot be located to sign a deed, the seller will hire an attorney to file an Action to Quiet Title.
The attorney will take the matter to a judge. The judge will order that advertisements be placed in search of the missing cousin or heirs. After a prescribed time has expired, the attorney goes back to the judge to report that no one responded to the ads, and the judge issues an Order extinguishing the rights of the parties, thus quieting title.