Because it reacts identically to C-12 and C-13, C-14 becomes attached to complex organic molecules through photosynthesis in plants and becomes part of their molecular makeup.
Animals eating those plants in turn absorb Carbon-14 as well as the stable isotopes.
Atoms of the same element that have different numbers of neutrons are called isotopes. Most carbon on Earth exists as the very stable isotope carbon-12, with a very small amount as carbon-13.
Here’s an example using the simplest atom, hydrogen. Carbon-14 is an unstable isotope of carbon that will eventually decay at a known rate to become carbon-12.
Libby in 1949, and has become an indispensable part of the archaeologist's tool kit since.
Radiocarbon, or Carbon-14, dating is probably one of the most widely used and best known absolute dating methods. Radiocarbon dating relies on a simple natural phenomenon.
This allowed for the establishment of world-wide chronologies.
So, we have a “clock” which starts ticking the moment something dies.
Obviously, this works only for things which were once living.