A subdivision surface is a polygon mesh that has been divided into more faces while retaining the object's general shape. You perform subdivision to add detail to an object, or to smooth it out.
OpenSubdiv modifier with Iterations = 0, 1, 2, 3 (left to right), with creasing applied along the centerline
3ds Max supports three kinds of subdivision surfaces:
Related closely to these are the Subdivision Surface rollout controls for editable poly objects, with which you can subdivide a surface without the need for a modifier.
The latter type works best as a finishing tool for models.