In theory, moving edit points would be an excellent way to edit a curve, since they lie on the curve itself. Unfortunately, it doesn’t work out that way. This is because the shape of the curve determines the positions of edit points, not the other way around. Alias does allow you to move edit points by “reverse engineering” the curve from the edit point. When you move an edit point, the Move tool tries to find a curve which passes through the new edit point location. Because this process is time-consuming and has an infinite number of solutions, the tool must place constraints on how moving the edit point affects the curve. Because of these constraints, you usually cannot make major changes well by moving edit points. Moving edit points is best for small scale reshaping. The only way to reshape the curve with complete power is by moving CVs.
There are, however, a few tasks that use edit points:
If you want more control in a curve, you can insert an edit point to increase the number of spans in the curve and give you more CVs to work with.
You can also delete edit points to decrease the number of spans in a curve (and probably change the shape of the curve).
It is possible to move edit points to change the shape of a curve, but avoid doing this except for minor adjustments.
Alias does not actually move the edit point itself, but instead moves the CVs to reshape the curve so the edit point is where you specified.