Radioactive dating can be done by analyzing the fraction of carbon in organic material that is carbon14.
The ratio of carbon-14 to carbon-12 in the atmosphere has been roughly constant over thousands of years. A living plant or tree will be constantly exchanging carbon with the atmosphere and will have the same carbon ratio in its tissues.
When the plant dies, this exchange stops. Carbon-14 has a half-life of about 5730 years; it gradually decays away and becomes a smaller and smaller fraction of the total carbon in the plant tissue. This fraction can be measured, and tissue age deduced.