Thoron radiation is a type of radiation with many uses.
It was used primarily as a method of interfering with sensors and transporter systems, (DS9: "Emissary", "The Way of the Warrior"; VOY: "Basics, Part II", "The Cloud") seen as a byproduct of alien appearances, (DS9: "If Wishes Were Horses"; VOY: "Sacred Ground") used for medical purposes, (VOY: "Basics, Part II", "Flashback") and used as a basis for weaponry (although it could result in instability in the weapon). (VOY: "Retrospect", "Warlord")
Antithorons can be generated on a large scale by Intrepid-class starships and have been used both to interfere with force fields and decontaminate planetary crusts prior to mining. (VOY: "Hunters", "Tattoo") Thoron radiation may also hinder transporter operations, presumably by interfering with sensor readings.