Absolute dating is used to determine a precise age of a fossil by using radiometric dating to measure the decay of isotopes, either within the fossil or more often the rocks associated with it.
For example, a problem I have worked on involving the eruption of a volcano at what is now Naples, Italy, occurred 38500 years ago with a plus or minus of 300 years.
So, when the materials are appropriate and one carefully avoids contamination and re setting radiometric clocks can be VERY ACCURATE.
The half-lives of several radioactive isotopes are known and are used often to figure out the age of newly found fossils.
Different isotopes have different half-lives and sometimes more than one present isotope can be used to get an even more specific age of a fossil.
(The nucleus of an atom is made up of protons and neutrons.) For example, the element carbon, which always has six protons in its nucleus, has three isotopes: one with six neutrons in the nucleus, one with seven, and one with eight.
Some isotopes are stable, but some are unstable or radioactive.
There are many radiometric clocks and when applied to appropriate materials, the dating can be very accurate.
As one example, the first minerals to crystallize (condense) from the hot cloud of gasses that surrounded the Sun as it first became a star have been dated to 4568 plus or minus 2 million years....!! Other events on earth can be dated equally well given the right minerals.
One way that helps scientists place fossils into the correct era on the Geologic Time Scale is by using radiometric dating.