Sorry, it was late, and I had the best of a bottle of Barossa valley shiraz inside me. In plain language, Goedel's theorem says that in a formal mathematical system there are theorems that are true, but cannot be proved within the system, and theorems that are false that cannot be disproved within the system. This is really to do with artificial intelligence, or, at least, what is required for artificial intelligence. We can solve problems by stepping outside the system and taking a look at how the system itself works. Computers can't do this unless their software is able to look at the working programme (the formal system) from a higher level.
Only connection with ATPL exams is the running decision whether to teach the truth ( but "What is truth?, said jesting Pilate, and would not stay for an answer") or some simplified sub-truth that gets the right tick in the box.
Us instructors lie awake at night worrying about this.
Recommend "Goedel, Escher and Bach - an eternal golden braid", by Douglas R Hofstadter
Dick W