Paradox
A paradox is a statement that appears to contradict itself but reveals a genuine truth when examined — 'the more carefully she explained, the less anyone believed her'.
The more carefully she explained, the less anyone believed her. The sentence should not be able to be true. It is, and working out why is the reader doing the thinking the sentence wanted them to do.
That is the mechanism. A paradox stops a reader for a second, and the second is the point: the contradiction forces the meaning to be reconstructed rather than received.
Orwell gives the most famous political example in Nineteen Eighty-Four — war is peace, freedom is slavery, ignorance is strength — where the form is turned against itself, and the shape that usually signals hard-won insight is used to signal a lie. That is worth remembering as a caution: like chiasmus, a paradox can make an empty claim sound earned.
Keep it apart from the two things nearest it. An oxymoron is a two-word contradiction inside a phrase. A paradox is a whole statement, and it resolves. Antithesis is a balanced contrast with no contradiction at all.
Used well in fiction, a paradox is usually a character stating the thing the book is about, some way before the reader is ready to agree with them. It should be earned by the story rather than asserted by the narration, or it reads as an author being clever within earshot.