It was developed in the 1950s by a team of scientists under Professor Willard F. Libby received the Nobel Prize in Chemistry "for his method to use Carbon-14 for age determinations in archaeology, geology, geophysics, and other branches of science." in 1960.
First a word on how the name of this method is written.
The C14 is a isotope of carbon, which is otherwise C12 or C13.
The C means carbon, the number gives the atomic weight rounded.
"Everything which has come down to us from heathendom is wrapped in a thick fog; it belongs to a space of time we cannot measure.
We know that it is older than Christendom, but whether by a couple of years or a couple of centuries, or even by more than a millenium, we can do no more than guess." [Rasmus Nyerup, (Danish antiquarian), 1802 (in Trigger, 19)].
Oakley (1979) suggested its development meant an almost complete re-writing of the evolution and cultural emergence of the human species.
The C-14 Method or Radiocarbon Method is the oldest physical method, which allows to determine the age of an object, if it contains carbon.
The method is named after its principle, it is based on the natural radioactive decay of the carbon isotope C14.
The unstable Carbon-14 within the organism begins to decay to form Nitrogen-14 by emitting a beta particle.
Over time there is a gradual decrease in the amount of Carbon-14 and the ratio of Carbon-14 atoms to other Carbon atoms declines. Therefore half of the Carbon-14 has decayed after 5730 years.