From LightWiki

A Subdivision surface is a group of Polygons (called the Cage) which are subdivided to make the object smoother. This means by modelling/animating a relatively small number of polygons, you can get a smooth shape. You can mix subdivision surfaces with other polygon types within the same object. To turn a selection of polygons into a subdivision surfaces, in Modeler select the polygons you wish to change, and press the 'Tab' key. To turn them back, press 'Tab' again. Obviously, because this uses the same button, if you have no polygons selected, and you have mixed polygons and sub-d surfaces, pressing tab will switch one set to sub-d surfaces, and the other to polygons and pressing 'Tab' will change them back again.

In LightWave there are two types of subdivision surfaces, Subpatches and Catmull-Clark (CC) patches.You can change how smooth a sub-d surface is in Modeller by opening the Modeler Options Panel and changing the Subpatch divisions and Catmull-Clark level values. To change it in Layout, open the Object Properties Panel and go to the Geometry tab. There you'll find Display Subpatch Level and Render Subpatch Level. This gives you the ability to use less sub-division for better interaction while animating, but much finer smoothing for your final render.

Subpatch

Subpatching is the way Lightwave originally did this, and as a result of this, it is a lot more efficient and faster to work with than CC patches. With Subpatches, you can sharpen the points of the cage with the Subpatch weight vertex map and using the Set Map Value and Airbrush tools.

Catmull-Clark patches

The novice to CC patches will think they are inordinately slow. While it is true that they can be slower than subpatches, a lot of the slowdown is because users think they are subdivided in the same way as LightWave's own subpatches, which is not the [[1]]. Catmull Clark subpatches don't have the ability to weight points, however you can weight the edges of a patch, which can be more useful. Although more useful it is also fairly limited on when you can do it since operations like mirroring and bandsawing currently (as of 9.3.1) break edge weighting.