radioactive dating does show that the Earth is billions and not thousands of years old, refuting young-Earth creationism.
A process for determining the age of an object by measuring the amount of a given radioactive material it contains. If one knows how much of this radioactive material was present initially in the object (by determining how much of the material has decayed), and one knows the half-life of the material, one can deduce the age of the object.
Note: The best known example of radioactive dating employs carbon 14, a radioactive isotope of carbon.