What does the title mean ? "That Was the Molecular Biology That Was"
An alternate title with similar meaning would be something like:
"How molecular biology was researched and studied before now".
There is a hint in your author's title that methods and perhaps topics in molecular biology have substantially changed now, and he is going to review what they used to do and how they did it.
For instance, if the author was writing his article, say in 2010, then he would be describing the study of molecular biology of an earlier age - perhaps 20 years earlier, maybe more, maybe less - depends on context. But, the author is going to discuss these earlier researchers, what they studied and perhaps how they did it.