Non euclidean geometry is any geometry that doesn't obey Euclid's axioms. Space itself is non-Euclidean (as far as the Moon cares it's moving in a straight line, but Earth is somehow always off to the side). The distance between A and B is always growing, and it's possible that if you go far enough in a straight line you'll end up back where you started. Spheres are Euclidean but any shape on their surface plane is not.

People mostly use non-Euclidean geometry as a shorthand for weird video game maps