As mentioned in the lesson, the era of thermal refining was during 1910 to 1940. This refining process was used to increase the yield of gasoline, kerosene, and diesel from petroleum through conversion processes as the demand for these fuels increased (particularly for gasoline during World War I). The era of catalytic refining was during 1940 to 1970, spurred by the onset of World War II.
During this time, higher performance gasoline was necessary so thermal conversion processes (characterized by free radical reactions) were replaced by catalytic conversion processes (characterized by ionic reactions). These catalytic processes included cracking, reforming, alkylation, and polymerization. As mentioned in the lesson introduction video, something that I found very fascinating was that what was initially a very competitive market among oil companies before WWII suddenly changed when everyone (in the Allied forces) joined together in a combined effort to produce better refining processes. This in turn developed higher quality (higher octane) and more powerful fuel for the war effort.
Interestingly, the German opposition originally developed synthetic oil by utilizing processes such as the Fischer-Tropsch process and Bergius process through coal gasification. They developed aviation/jet fuel, oils, and rubber among other things throughout WWII. Source: http://en.wikipedia.org/wiki/Synthetic_fuel.