It works because we know the fixed radioactive decay rates of uranium-238, which decays to lead-206, and for uranium-235, which decays to lead-207.
For example, uranium-lead dating can be used to find the age of a uranium-containing mineral.
The thing that makes this decay process so valuable for determining the age of an object is that each radioactive isotope decays at its own fixed rate, which is expressed in terms of its half-life.
So, if you know the radioactive isotope found in a substance and the isotope's half-life, you can calculate the age of the substance. Well, a simple explanation is that it is the time required for a quantity to fall to half of its starting value.
So, you might say that the 'full-life' of a radioactive isotope ends when it has given off all of its radiation and reaches a point of being non-radioactive.
When the isotope is halfway to that point, it has reached its half-life.