What is the ​ "this effect" ​ that doesn't remove White Ward?
It refers just to the protection granted by White Ward, not protection granted by other effects.

The easiest way to see this is just to look at another similar card, Spectra Ward:


  Enchanted creature gets +2/+2 and has protection from all colors. This effect doesn't remove Auras.


That's the same language as White Ward, and it has a ruling in Gatherer:


  The protection granted by Spectra Ward won’t cause any Aura to be put into its owner’s graveyard, including Spectra Ward itself. However, if the enchanted creature gains protection from white in another way, Spectra Ward will be put into its owner’s graveyard as a state-based action.