The CO2 is taken up by plants during
photosynthesis and animals eat the plants for food. Some animals
also eat other animals for food. In the long run, according to
Libby, living organisms develop a "steady state"
concentration of
C-14 in them. Measurements of the ratio of C-14/C-12
place it at 1 in 1012 atoms. So there's not very much.
Once an organism dies, its carbon
cycle with the environment stops. As the carbon-14 slowly decays
(by beta emission) it is not replaced. Thus the 1/1012
ratio gradually decreases. By carefully measuring the current
ratio in a sample and comparing it to the "steady-state"
ratio in a living organism scientists can estimate when the
organism died. For plant material used in artifacts, such as
cloth or canvas, this gives an approximate "age". 
