"Box modeling is a technique in 3D modeling where the model is created by modifying primitive shapes in a way to create a "rough draft" of the final model. This is in contrast with the edge modeling method, where the modeler edits individual vertices. While a primary function of box modeling involves extruding and scaling the flat planes that make up a model, called faces, another, more prominent feature of this art style gives it a second, less rudimentary name of subdivision modeling." via Wikipedia.
Subdivision modeling is derived from the idea that as a work is progressed, should the artist want to make his work appear less sharp, or "blocky", each face would be divided up into smaller, more detailed faces (usually into sets of four). However, more experienced box modelers manage to create their model without subdividing the faces of the model. Basically, box modeling is broken down into the very basic concept of polygonal management.
I tried to use this type of modeling for a small furniture project. I worked shifting the points of primitive box and extruded its sides, I added more segments in subdivisions faces with the cut tool and slice plane when needed and working with turbosmooth tool to reach the desired degree of curvature of my design. The model was built with 3dmax, the next step will be to increase the complexity of design and the use of new division tools of faces.