Smoothness Level

The smoothness level for a smesh sets how smooth the transition will be on the smesh for each face and between faces. Smoothness works by creating hidden subdivisions of the surface. The higher the level is set the higher the number of subdivisions.
The Smoothness level can be set from the minimum of one to the maximum of 4. A cube set to one tessellation in all values will look like this when the Smoothness level is set to 1: And Like this when the smoothness level is set to 4:      

...