Not sure what this process does to help hold an edge but it does force a patina that protects a carbon steel knife blade.
The physics are as follows;
The starch in the potato oxidized. The Chlorogenic and Citric acid content in the potato worked on the starch resulting in various chemicals being produced including, but not limited to, Sodium Chlorate I and III and Hydrogen Peroxide. These chemicals then oxidize the steel in the knife in a similar process that is used in gun bluing.
Different types of potatoes will result in different patina. Different carbon content in the blade will also produce a different patina. No two will be alike.
This patina can also be forced by using horseradish mustard to to cause the chemical process. Using a flux brush to apply the mustard you can wind up with a patina that resembles Damascus steel.
Just don't forget to wash the knife after the patina level you want is achieved and then follow up with a good wax for even more protection. I find Renaissance Micro-Crystalline Wax Polish is about as good as it gets.
Have fun protecting your carbon knives!