I'm not an expert, but I'm sure I'll be corrected if I'm way off base.
The carbon in the carbon dioxide in the atmosphere is a relatively consistent mix of carbon-12 and carbon-13, because solar radiation hitting the atmosphere converts C12 to C13 at a more or less constant rate.
All carbon-based life makes use of atmospheric CO2 to get it's carbon, so our C12/C13 ratio is about the same as that of the atmosphere.
As soon as something gets cut off from the atmosphere because it's been buried, mummified or whatever the carbon dating clock starts ticking as C13 decays and is not replaced. So until almost all the C13 is gone you can date organic material or trapped air by the proportion of C13 it contains.
Carbon dating gets unreliable and eventually stops working past a certain point - I vaguely recall that it's in the tens of thousands of years, but that's the best I can do offhand.