This is how carbon dating works: Carbon is a naturally abundant element found in the atmosphere, in the earth, in the oceans, and in every living creature.
C-12 is by far the most common isotope, while only about one in a trillion carbon atoms is C-14.
It takes another 5,730 for half of the remainder to decay, and then another 5,730 for half of what's left then to decay and so on.
The period of time that it takes for half of a sample to decay is called a "half-life." Radiocarbon oxidizes (that is, it combines with oxygen) and enters the biosphere through natural processes like breathing and eating.
Specimens which lived and died during a period of intense volcanism would appear older than they really are if they were dated using this technique.