This option is enabled only with Console Programs.
Console programs have one annoying feature: they close immediately after they are finished. So the text output simply rushes by and the console window closes before you can inspect the output. To avoid that, PA-RUN has two options: Capture Output and this option "Keep console window open".
But while "Capture Output" hides the console window by redirecting it to its internal component, this option "Keep console window open" runs the console program through cmd.exe which is itself a visible console program which stays open even after the console program itself terminates.