Radiocarbon dating how stuff works
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".
It was the first absolute scientific method ever invented: that is to say, the technique was the first to allow a researcher to determine how long ago an organic object died, whether it is in context or not.
Cave deposits and varves have the potential to include old soil carbon, and there are as-yet unresolved issues with fluctuating amounts of C14 in ocean corals.
By measuring the trace amounts of radioactive carbon-14 (so named because it has 6 protons and 8 neutrons) in a dead something and comparing it to the amount of regular carbon-12 (6 protons and 6 neutrons) you can figure out how long it’s been since that sample was alive.
Carbon-14 is continuously generated in the upper atmosphere when stray neutrons bombard atmospheric nitrogen (which is what most of the atmosphere is).
Since that time, CALIB, now renamed Int Cal, has been refined several times--as of this writing (January 2017), the program is now called Int Cal13.
Int Cal combines and reinforces data from tree-rings, ice-cores, tephra, corals, and speleothems to come up with a significantly improved calibration set for c14 dates between 12,000 and 50,000 years ago.