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It is radioactive, meaning that it slowly decays (and turns into nitrogen).
The air is full of a more-or-less constant amount of carbon-14, and plants take it up via photosynthesis; animals eat that plant and acquire the same levels of carbon-14 (and carnivores eat herbivores and acquire carbon-14 as well).
Experimental evidence has built up over time to give a "calibration curve", a good set of measures of what this carbon level was, which in turn allows fairly decent estimates of dates Radiocarbon dating gets a lot more complex when you scratch under the surface.
To find the age of things older than that we would need a different radiometric dating method Carbon-14 is a type of carbon (a very common element) with 8 neutrons.
Thus, all living things on earth at any given moment contain about the same amount of carbon-14.
When you die and stop eating, that amount of carbon-14 is locked in - you don't take any more into your body.
Once the organism dies there is no new carbon-14 being cycled into the cells and knowing the rate of decay (half life) of carbon-14 you are able to work back to an approximate date of death.
Many human activities such as coal power plants and nuclear testing have increased the amount of carbon-14 in the environment.