While a carbon based life form is alive it takes up carbon from the environment and incorporates it into its structure. A certain percentage of this carbon is going to be the radioactive isotope carbon 14; the standard, stable form is carbon 12. Carbon 14 is Nitrogen 14 that, through the magic of nuclear physics has temporarily decided to become carbon, but will slowly decide to go back to being nitrogen. A given sample of carbon 14 will have half its atoms decide to revert in 5730 years, but, as long as the organism is alive it replenishes its carbon supply with available carbon. Once dead, it stops taking up environmental carbon and the clock starts ticking. By examining the ration of carbon 14 to carbon 12 in the sample, carbochronologists can roughly date a specimen. This is based on several assumptions, not the least of which is that the ratio of carbon 14 to carbon 12 tens of thousands of years ago was the same as it is now. As y'all have correctly sussed, this dating of ivory will only tell you when the animal that the ivory came from died. If the artifacts being dated were discovered in ashes from a prehistoric fire, then the date of the fire can be determined. This could give us supporting evidence for the date, if the dates of the fire and the ivory match.
