This carbon-14 labeled carbon dioxide is taken up by plants in their normal process of photosynthesis.
Animals and people that eat these plants take the carbon-14 into their bodies as well.
Nitrogen normally occurs in a seven proton, seven nuetron, nitrogen-14 state.
When it collides with an energetic neutron it becomes carbon-14, with six protons and eight neutrons and gives off a hydrogen atom with one proton and zero neutrons. Carbon-14 is an isotope of carbon, which exists only is small amounts in the environment (1 in one trillion carbon atoms is carbon-14).
Carbon dating is used to determine the age of biological artifacts up to 50,000 years old.