When you create a Bézier curve on a surface, a relationship is created between the curve point and the surface it lies on. This relationship is useful when editing the point and the surface.
To create a Bézier curve on a surface:
The word In is attached to the cursor when the input point is projected onto the surface and the word On at positions on surface curves.
The curve points on the surface have the same tangents as the surface points on which they lie.
In the example below, you can see that the tangency of the curve matches the surface. If you want the curve to flow along the exact shape of the surface, you may need to put in extra points along the curve.
Any curve point, that does not lie on the surface, has no relationships.
The curve is now ready to edit to your requirements.