Carbon has a weight of twelve atomic mass units (AMUs), and is the building block of all organic matter (plants and animals).
A small percentage of carbon atoms have an atomic weight of 14 AMUs. Carbon-14 is an unstable, radioactive isotope of carbon 12.
The halflife of carbon 14 is 5730 ± 30 years, and the method of dating lies in trying to determine how much carbon 14 (the radioactive isotope of carbon) is present in the artifact and comparing it to levels currently present in the atmosphere.
Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.
The radiocarbon dating method is based on the fact that radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire in a sample from a dead plant or animal such as a piece of wood or a fragment of bone provides information that can be used to calculate when the animal or plant died.
Other corrections must be made to account for the proportion of throughout the biosphere (reservoir effects).