What would be an example of one of Niels Bohr's "great truths"?

Niels Bohr (one of the pioneers of quantum theory) was a veritable gusher of pithy quotes. Almost any collection of his quotes includes some variation on the following: “There are trivial truths and there are great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.” (he seems to have restated this on several occasions, in slightly different forms).

How do you understand this? Can you give an example of a truth that would qualify as “great” by this standard?