The primary use of carbon dating in archaeology is to determine the age of organic materials by measuring the decay of the radioactive isotope carbon-14. This method is effective for dating artifacts, bones, and fossils that are up to about 50,000 years old. By analyzing the ratio of carbon-14 to carbon-12 in a sample, archaeologists can estimate how long it's been since the organism died. This tool is invaluable for understanding historical timelines, ancient civilizations, and the progression of human activity throughout prehistoric times.