Carbon has several isotopes. Carbon 12 is the stable variety, radioactive Carbon 14 has a half life of just under 5800 years. Any living organism takes in both radioactive and non-radioactive carbon, either through the process of photosynthesis, or by eating plants or eating animals that have eaten plants. When the animal dies, however, uptake of carbon stops. As a result, radioactive carbon atoms are not replaced as they decay, and the amount of this material decreases over time. The rate of decrease is predictable and can be described with some accuracy, increasing our ability to perhaps date the biological events of our planet.
A famous experiment was done in the 1970’s to date the Turin Shroud.
Carbon 14 is produced in the upper atmosphere when cosmic radiation from space interacts with nitrogen gas, converting nitrogen 14 to carbon 14. These carbon 14 atoms combine with oxygen to form carbon dioxide gas, which is absorbed by plants. We don’t actually know for sure if the rate of carbon dioxide formation has stayed constant over time, however, It’s usually quoted as a “small part of less than 1%” The difference casts doubt on the accuracy of the method.