Nuclear testing in the middle of the twentieth century threw up lots of carbon-14 in the atmosphere. It has been slowly washing out since then. Because we have measured the amount of carbon-14 every year, we can use the amount of carbon-14 in it to simply look up (approximately) what year some plant material grew up in. This version of carbon-14 dating has nothing to do with the nuclear-decay-based carbon-14 dating that most people are familiar with, which acts over thousands of years.