Approximation nodes give you more precise control over all of mental ray for Maya approximation features, some of which Maya cannot access. For example, you can use Approximation nodes to specify separate tessellation settings for surfaces, trim curves, and displacement maps.

As an example, consider a simple flat NURBS surface with a complex trim curve. For such a case, you would specify a low-quality surface approximation in conjunction with a high-quality trim curve approximation. mental ray would then ensure that the surface is approximated with only a few triangles except around the trim curves, where many triangles would be used to ensure a smooth edge.

The same analogy applies to a simple surface with a complex displacement map. For that case, you might apply a low-quality regular surface approximation in conjunction with a high-quality displacement approximation, to ensure that triangles are added only to areas where they are needed to capture the complexity of the displacement map.