From reverse engineering normalized power that I see in Strava, TrainingPeaks and other places it looks like the number derived is what constant power you'd need to output to equal the same training stress score.
Example: Ride at a constant 100% of FTP for one hour and 50% of FTP for one hour. Your training stress is 125. 100 from the 100% effort (1.00x1.00x100) and 25 from the 50% effort (0.50x0.50x100). Your average power for this ride is 75% of FTP. If you maintained a constant power and wanted to achieve a training stress of 125 you can reverse the formula. 125/2 hrs = 62.5 stress/hour. Divide by 100 = 0.625. Take the square root = 0.625^0.5 = 79.1% of FTP.