Propeller-driven aircraft perform best at subsonic speeds (slower than the speed of sound). This is because the blade tips of the propellers approach the speed of sound at faster speeds, and this greatly increases the drag on the propeller blades, among other things. This is why after World War 2 propeller-driven fighter craft fell out of use, since they could not get much faster without major issues.
Modern passenger jets operate in the transonic range (0.7 to 0.8 times the speed of sound). This range is a bit too fast for propellers and pretty much requires jet engines or something similar. Using props for passenger planes would reduce their speed as experienced by passengers today. I believe this is what the author is referring to.
