It shouldn't be a hard question to answer though, should it? If it is, that kind of speaks for itself.
I don't know enough about Scientology to answer it for Scientology. In general though, my guess would be the kind of information that, while changing nothing, changes everything.
Here's a poor example of what I mean. You find out your father wasn't really your father (long after everyone involved but you is dead). The only thing changed is how you view your own history, nothing you can measure in a material sense is changed.
Or, you find out space aliens really did land in Roswell. You get convincing evidence, but, like so many episodes of the X Files, it isn't preserved. Nothing changes, but the way you look at things change.