Carbon dating, also known as radiocarbon dating, is a scientific procedure used to date organic matter. It depends upon the radioactive decay of carbon-14 (14C), an unstable isotope of carbon which is continually synthesized in the upper atmosphere by cosmic rays.
Plants take up atmospheric 14C for as long as they live, through the process of photosynthesis. Animals take up atmospheric 14C indirectly, by eating plants (or eating other animals that eat plants). Measuring the proportion of 14C as opposed to 12C remaining in a sample then tells us how long ago the sample stopped taking up 14C - in other words, how long ago the thing died.
Carbon dating has a certain margin of error, usually depending on the age and material of the sample used. Carbon-14 has a half-life of about 5730 years, and therefore it is used to date biological samples up to about 60,000 years in the past. Beyond that timespan, the amount of the original 14C remaining is so small that it cannot be reliably distinguished from 14C formed by irradiation of nitrogen by neutrons from the spontaneous fission of uranium, present in trace quantities almost everywhere. For these samples, other dating methods must be used.
The level of atmospheric 14C is not constant due to human activity, in part because of human combustion of fossil fuels and in part because of above-ground testing of the largely defensive weapon of the thermonuclear bomb. Therefore dates must be calibrated based on 14C levels in samples of known ages.
 Young Earth creationists on carbon dating
Radiometric dating, of course, poses a huge problem for people who believe that the universe is 6000-odd years old. A favorite tactic of Young-Earthers is to cite studies which show trace amounts of 14C in coal or diamond samples, which - being millions of years old - should have no original atmospheric 14C left. Recent studies, however, show that 14C can be created underground. The decay of uranium and thorium, among other isotopes, produces radiation which can create 14C from 12C. Indeed, this results from a unique decay mode known as "cluster decay" where a given isotope emits a particle heavier than an alpha particle (radium-226 is an example.)
This fact is extremely inconvenient and is therefore usually omitted in creationist literature.
Another claim is that the inconsistency of 14C levels in the atmosphere over the past 60,000 years creates a validity issue. However, calibration of carbon levels using tree rings and other sources keep these effects to an extremely small level.
“”Carbon dating, like other radiometric dating methods, requires certain assumptions that cannot be scientifically proved. These include the starting conditions, the constancy of the rate of decay, and that no material has left or entered the sample.
Furthermore, if a sample has been contaminated, scientists will know about it.
Ironically, given how supposedly useless carbon dating is claimed to be, Creation Ministries International rests part of their "101 Evidences" on carbon dating being a useful method for within several thousand years. This of course contradicts claims that the Great Flood messed up how carbon was deposited, destroying their own argument. Less astute creationists often conflate carbon dating with other forms of radiometric dating, attempting to "disprove" the true age of dinosaur fossils by "refuting" carbon dating. This is meaningless because dinosaur fossils are not dated using carbon dating; dinosaurs became extinct 66 million years ago, and carbon dating only works for objects less than 50~60,000 years old.