You almost only meet this word inside the humorous phrase a whole nother. People say it when they want to stress that something is a completely different matter from the one you were just talking about: That’s a whole nother story. It is playful, spoken American English, not for a formal essay. The mess is the point: another is really an + other. Speakers wanted a whole other…, then treated another as a + nother so they could drop whole in the middle — a whole nother thing — the way you might say a whole other thing. Learner dictionaries call it a changed form of another whole. Though actually, English also has an old dialect word nother meaning “neither”, from Old English nōhwæþer (compare neither). That is a different word that happens to look the same on the page. The joke you will hear is the split of another, not that old “neither”.