radioactive dating does show that the Earth is billions and not thousands of years old, refuting young-Earth creationism.
A method for determining the age of an object based on the concentration of a particular radioactive isotope contained within it. For inorganic materials, such as rocks containing the radioactive isotope rubidium, the amount of the isotope in the object is compared to the amount of the isotope's decay products (in this case strontium). The object's approximate age can then be figured out using the known rate of decay of the isotope. For organic materials, the comparison is between the current ratio of a radioactive isotope to a stable isotope of the same element and the known ratio of the two isotopes in living organisms. Radiocarbon dating is one such type of radiometric dating.
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.