The UV mapper essentially projects a bunch of UVs onto the selected mesh and it previews the effects live while it's active (there's a whole other thread on this...).
The 3D coordinates affect the center of the projection. Usually you want it centered on the object you're working with, so just click "Center Projection". Next, the UV mapper doesn't actually do anything (i.e. make the preview real) until you click "Write UV Coordinates".
In general, the spherical mapping works well for roughly spherical objects (but not for C3D's spheres! see below); the box mapping works well for boxes, cubes, simple houses; cylindrical mapping works well for cylinders; and planar mapping works really well if restricted to a selection of roughly coplanar faces (you can then "stamp" all or part of a texture onto the selection). This latter technique is used in my coffee cup tutorial.
The 2D coordinates scale or offset the UV map (UV maps are always 2D, although in theory you can have 3D UV maps, C3D doesn't support them; C3D only supports 3D spatial mapping).
Aside on Spheres
The standard spherical mapping is pretty much borked on C3D's standard spheres — you can see it if you convert one to editable and look at its UV map. Parts of the material are simply ignored near the poles. This is because the UV-mapping spheres "nicely" is impossible, and "effectively" is very hard. (Maybe a tutorial on its own.)
Illustrations top-to-bottom:
- Spherical Projection restricted to selection (the sphere-like part of the mesh).
- Bad things happen at the poles. (Thank goodness for the icecaps, am I right?)
- Planar Projection scaled down a bit from default settings
