A lot of evolutionary science talks about energy expenditure. For an animal to survive it needs to take in at least as many calories as it expends, so evolutionary scientists often explain behavior in terms of expending calories and preserving calories. E.g, Predators tend to sleep a lot because hunting takes up a lot of calories. It's better to preserve the calories they gained hunting by sleeping a lot, rather then spend them on another hunt that may or may not be successful. As opposed to large herbivores that don't gain that many calories from grass, but don't spend so many eating it, either. They sleep very little because foraging those extra hours turns out to be a caloric win.
Our "ancient" brain (which is a crappy term, I know) refers to the set of behaviors we evolved to survive in a society pre civilization. In that environment, effort == calories spent. What the author is saying is that for evolutionary reasons, we evolved to not want to waste calories (put forth effort) if there isn't a good chance of getting them back. But, because our food sources no longer in jeopardy, that evolutionary urge which led to our survival in the wild now leads to the vice known as procrastination.