The "molecular" part refers to the use of molecular data for the number of amino acid or DNA base changes between "related" molecules in species whose time of divergence can be "determined" using this agreed-to standard. Thus if the genes for cytochrome C (actually the technology is now very sophisticated and only specific types of proteins believed to give "normal" responses are used) of two forms that are believed to have diverged 100 million years ago differ by 20 bases, the rate of change for those two species would be 1 base change per 5 million years in that particular gene.
If we find modern forms for which molecular differences have been determined, believed to have been linked by a common ancestor, the time can be estimated using the number of observed changes and the calibrated rate of change. The assumptions are legion: that the changes are due to random mutations, and are not functional differences appropriate for the organisms; that the changes in fact did take place (i.e. that evolution is the explanation for the differences); that we know the time of divergence at least for the forms used for calibration, that we know the evolutionary relationships between different forms with some degree of finality; that we have chosen the "correct" molecular differences to measure; etc. In fact, many different rates can be found depending on which particular molecules are compared. This leads to a kind of selection to get the results that favor the biases of the investigator that must be carefully considered.
2010 Arthur V. Chadwick, Ph.D.