The hardest section of a route or boulder — it usually determines the whole grade.
A 7a is rarely 7a throughout; usually two or three moves carry the whole thing and the rest is markedly easier. Which is why the tactical question isn't 'how do I climb the crux?' but 'how do I arrive there as fresh as possible?' Experienced climbers deliberately conserve strength beforehand, find the last rest position and breathe out there before committing. Second point: at the crux footwork almost always decides it, not arm strength — if you start hauling yourself up at that point, you're already too late.