Nuclear reactors produce radioactive by-products that decay at different rates. One common by-product is iodine-131 which has a half life of about 8 days while another is cesium-137 with a half life of about 30 years.
When a reactor switches off, the iodine decays more quickly so the ratio between these two isotopes changes rapidly over a period of days. That’s why measuring this ratio is a good way to work out when the nuclear reactions terminated.
There are some complicating factors, however. The most important of these is that the ratio of iodine-131 and cesium-137 to start with depends on how long the reactor has been operating and so is not constant.