Radiometric Dating is the determination the date at which materials were formed by analyzing the decay of radioactive isotopes that were incorporated into the material when it was created. Probably the best known form of radiometric dating is Carbon 14 dating.
Most materials are radioactive to some extent, but the decay rates of most are so long that for all practical purposes, they can be considered to be inert. The remiander are said to be "Radioactive". Radioactive materials can decay in any of several ways emitting either a particle or radiation and changing to a different element or isotope. The decay rate of radioactive materials does not depend on temperature, chemical environment, or similar factors. For dating purposes, the important paramater is the "half life" of the reaction -- the time it takes for half the material to decay. Half lives of various isotopes vary from microseconds to billions of years. Materials useful for Radiometric dating have half lives varying from a few thousand years to a few billion years.
Radiometric dating assumes that the initial proportions of a radioactive substance and its decay product are known. The decay product should not be a small molecule gas that can leak out, and must itself has a long enough half life that it will be present in significant amounts, and the initial element and the decay product should not be produced in significant amounts by other decay reactions. The chemistry/physics to isolate and analyze the reaction products must be straightforward and reliable.
A number of systems are known that satisfy these constraints including Carbon14-Carbon12, K-Ar; Ar-Ar; and U-Pb. Carbon14 has a fairly short half life and is used for dating recent organic remains. It is useful for periods up to perhaps 60,000 years and is very important to historians and archeologists as a method of determining the age of human artifacts. The other methods have half lives of hundreds of millions of years, and are used for dating rock formations.