Always consider a model something you cut out and glued many small pieces of paper together, and filled with air. No air leaks! Just 1 outer connected surface.
Shapeways uses the model info sent to a machine process.Your model might render nice, but might be impossible to create.
The surface, while you can visualize it, has no thickness, so the faces/polygons that form it all have to be connected to make it manifold(water or air tight). Main point being it has to be sealed.
You can hollow it out to save cash, but that's another topic.
Doubles refer to vertices being at same Cartesian coordinates as other vertices forming exterior surfaces.Bad,bad. leads to printer errors.
With your modeling program, you just want to see all edges, faces,verts on the surface. Anything in its interior, in most cases will cause more problems.