When you create a curve point on a surface, a relationship is created between the curve point and the surface it lies on.
When you move or edit the surface, the curve points on the surface update too.
For example, when you move a point on the surface 
:
the curve changes as the surface changes shape:
When you edit the curve such that its points are within the surface, it remains on the surface. The edited curve points have the same tangents as the new surface points on which they lie.
For example, when you drag a curve point 
along the surface:
it remains on the surface and the tangents through it are updated too 
:
If you drag curve points off the surface, they lose their dependency.
If you drag a curve point back onto a surface, it gains a new dependency. Press and hold the Shift key to place a point inside a surface patch (ensure the word In is attached to the cursor to indicate the point is inside the patch).
To delete the dependencies:
- Right-click the curve and select Delete dependencies from the context menu.