This turns out not to be exactly true, and so there is an inherent error between a raw "radiocarbon date" and the true calendar date.
It can theoretically be used to date anything that was alive any time during the last 60,000 years or so, including charcoal from ancient fires, wood used in construction or tools, cloth, bones, seeds, and leather.
It cannot be applied to inorganic material such as stone tools or ceramic pottery.
The technique is based on measuring the ratio of two isotopes of carbon.
Carbon has an atomic number of 6, an atomic weight of 12.011, and has three isotopes: carbon-12, carbon-13, and carbon-14.
(The numbers 12, 13 and 14 refer to the total number of protons plus neutrons in the atom's nucleus.
Thus carbon-14 has six protons and eight neutrons.) Carbon-12 is by far the most abundant carbon isotope, and carbon-12 and -13 are both stable.
But carbon-14 is slightly radioactive: it will spontaneously decay into nitrogen-14 by emitting an anti-neutrino and an electron, with a half-life of 5730 years.
The theory behind radiocarbon dating is as follows: Why doesn't the carbon-14 in the air decay along with terrestrial carbon? The trick is that radioactive carbon-14 is continually replenished in a complex reaction that involves high-energy cosmic rays striking the upper atmosphere.
In this process, nitrogen-14 (7 protons and 7 neutrons) gains a neutron and loses a proton, producing carbon-14 (6 protons and 8 neutrons).
The proportion of carbon-14 to carbon-12 in the atmosphere therefore remains relatively stable at about 1.5 parts per billion.
One of the implied assumptions in radiocarbon dating is that levels of atmospheric carbon-14 have remained constant over time.