computer speak: just means given the set of axioms there is a method of examining them and then writing down a proposition which is consistent with the axioms, and whose negation is also consistent with the axioms. Meaning if we assume it true there are no contradictions, and if we assume its negation is true there are still no contradictions. Example, the continuum hypothesis and the axioms of ZFC (godel propositions are a little unrealistic; formally they are correct, but practically they aren't propositions you might come across 'naturally')

You've probably already heard about or even read it, but I recommend Godel Escher Bach by Douglas H. It was the only layman book I read that broke down Godels argument for me in an understandable fashion. I read it when I was like ten and it still made sense to me, despite my age. That is the sign of a good author, since the idea itself isn't at all intuitive or obvious, especially to a kid.