An extrusion path need not be a straight line. It can be a curve.

Here is a side view in parallel (orthographic) projection.

And here is a perspective view.

This should begin to get your imagination working a bit. If we can have a curve, we can twist it into a spiral.

A spiral is a very effective shape in 3-D graphics because it has so much coherent 3-D space information. Note how easy the shape is to "read" compared to the extruded curve above. Also notice that a hexagon has been extruded rather than a rectangle. This creates a faceted look.

We can close the extrusion curve to make a ring or torus.

The bracelet shape above was made by starting with a circle, stretching it out into an oval, and then extruding the oval along a circular path.

If the extrusion path is changed from a circle to an oval (much like the shape of the oval being extruded) we get the following:

The concept of extruding a polygon in a closed path, as we have just done, merges into the concept of "lathing." On a wood-turning lathe, as on a pottery wheel, the curved profile is cut into a solid object by turning the object. In a similar way, we can rotate a flat shape around an axis to create a solid object.

A side, orthogonal view of a lathed object reveals the original profile.

A perspective view from a different angle gives us a basic goblet shape. Lathing is the obvious method for creating this kind of curved symmetry.

It's one big mental step from extruding a single polygon to joining different polygons along an extrusion path.

We start with a regular hexagon, a six-sided polygon. At the other end of the extrusion path is a rectangle with the corners rounded. As the two polygons are joined by the extrusion path, the shape of the object is interpolated over the path. Here are a couple of different perspective views to help you make sense of the shape.

This concept of bridging between differently shaped polygons is called variously "skinning," or "lofting" or "morphing" depending on the context and the specific way the procedure is accomplished. Just as with the extrusion of a single polygon, the path may be curved, nor need the polygons be normal (perpendicular) to the path.