Smoothing groups define whether a surface is rendered with sharp edges or smooth surfaces.

Left: The bottle has no smoothing.

Middle: Smoothing is assigned only to the highlighted group of faces.

Right: The bottle is smoothed using three different smoothing groups: on the body, the neck, and the top edge.

Smoothing groups are numbers assigned to the faces or patches of an object. Each face or patch can carry any number of smoothing groups up to the maximum of 32. If two faces or patches share an edge and share the same smoothing group, they will render as a smooth surface. If they don't share the same smoothing group, the edge between them will render as a corner.

You can manually change or animate the threshold values for smoothing group assignments using such tools as Editable Poly (Polygon/Element) and the Edit Mesh modifier.