What is ellipsoidal height h in relation to the reference ellipsoid?

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Ellipsoidal height h is the distance from the point to the reference ellipsoid measured along the normal to the ellipsoid, i.e., how far the point lies above the ellipsoid surface. This is a measurement tied to the mathematical reference surface (the ellipsoid) rather than to the geoid. It differs from orthometric height, which is height above the geoid, and from geoid-related concepts like N (geoid undulation) where h = H + N. So the correct idea is that h represents the height above the reference ellipsoid, not from the geoid or below it, and not equal to orthometric height.