Geometric relationships are optional constraints that can be applied to the geometry of your 3D model. These constraints consist of things like:
1. Bonded surface edges
2. Fix an edit point to a curve or surface
3. Fix an edit point relative to another edit point
4. Fix a curve to a surface
5. Fix a surface edge to the middle of another surface
6. Connect two curves with ruling lines that update while editing the curves
These relationships are all dynamic in that they all update visually while you move any edit point. Relationships are powerful tools that allow you to do things like attaching a curve to a surface to define a trimming region for the surface. You can then dynamically drag the curve on the surface and watch how it changes the shape of the trimmed surface. Bonded surface edges allow you to dynamically edit multiply-connected surfaces (polysurfs) without having the surfaces separate.
The key points to be made about relationships in Pilot3D are that they are optional and that they are independent of the entities. This means that the relationships can be added or deleted at any time without affecting the shape of the related geometry. Generally, it is best to use relationships only when necessary, since over-constraining your model can create more problems than they solve.