All living things exchange the gas Carbon 14 (C14) with the atmosphere around them—animals and plants exchange Carbon 14 with the atmosphere, fish and corals exchange carbon with dissolved C14 in the water.Throughout the life of an animal or plant, the amount of C14 is perfectly balanced with that of its surroundings. The C14 in a dead organism slowly decays at a known rate: its "half life".Radiocarbon dating was invented in the 1950s by the American chemist Willard F.Libby and a few of his students at the University of Chicago: in 1960, he won a Nobel Prize in Chemistry for the invention.
Since it is chemically indistinguishable from the stable isotopes of carbon (carbon-12 and carbon-13), radiocarbon is taken by plants during photosynthesis and then ingested by animals regularly throughout their lifetimes.
Radiocarbon dating cannot be used for older specimens, because so little carbon-14 remains in samples that it cannot be reliably measured.
Creationists often criticize radiocarbon dating in the context of discussions of the age of the earth.
Given relatively pristine circumstances, a radiocarbon lab can measure the amount of radiocarbon accurately in a dead organism for as long as 50,000 years ago; after that, there's not enough C14 left to measure. Carbon in the atmosphere fluctuates with the strength of earth's magnetic field and solar activity.
You have to know what the atmospheric carbon level (the radiocarbon 'reservoir') was like at the time of an organism's death, in order to be able to calculate how much time has passed since the organism died.