The element carbon has two isotpes `^12C_6 and ^14C_6` .The difference is in the number of neutrons in the Carbon atom`^12C_6 has 6,^14C_6 has 8` .The `^14C_6` is known as radio active carbon.
When an organism is alive they are mostly made of `^12C_6` , but absorb a bit of `^14C_6` from the atmosphere, this amount is known. So a living organism has a known ratio of `^12C_6` to `^14C_6` .Once the organism dies, they can not absorb `^14C_6`from atmosphere.
Since `^14C_6` radioactive, so it s decays away at a fixed rate. So after a given period of time the organism will have the same amount of `^12C_6` as when it died, but some of the quantity of `^14C_6` will have decayed away. Since we know the rate of change, and the original percentage of `^14C_6`, we can calculate the time elapsed based on the current ratio of `^12C_6` to `^14C_6` .This process of detrminig age is know as carbon dating.