First, for carbon-14 dating to be accurate, one must assume the rate of decay of carbon-14 has remained constant over the years.
However, evidence indicates that the opposite is true.
For every one trillion carbon-12 atoms, you will find one carbon-14 atoms.
A small percentage of carbon atoms have an atomic weight of 14 AMUs. Carbon-14 is an unstable, radioactive isotope of carbon 12.
As with any radioactive isotope, carbon-14 decays over time.
There is then a ratio of carbon-14 to carbon-12 in the bodies of plants, humans, and other animals that can fluctuate, but will be fixed at the time of death. The premise behind the method is to determine the ratio of carbon-14 left in organic matter, and by doing so, estimate how long ago death occurred by running the ratio backwards.
After death, the carbon-14 would begin to decay at the rate stated above. The accuracy of this method, however, relies on several faulty assumptions.