This post is basically a brain-dump of what I currently know about hardware tesellation. I am hoping that my readers may find it interesting, and can help lend their expertise to expand on the topic in the comments..

DirectX 11 has added support for hardware tessellation. An overview is posted here on MSDN.

My understanding is that hardware tesselation can offer significant performance benefits by performing surface subdivison and displacement mapping on the hardware, thus increasing the amount of detail rendered while reducing the amount of data flowing through the pipeline. There is a sample demonstrating hardware tessellation also described on MSDN. A more indepth technical paper called Programming for Real-Time Tessellation on GPU by Tatarchuk et al. is also available from AMD, which also discusses the implications of hardware tessellation for asset creation pipelines. 

This is not the first API for performing hardware tesselation. There also is an ATI GPU tessellation library which works with DirectX 9 that you can download from AMD. Apparently the XBOX 360 supports hardware tesselation, but does not have the two new shader stages introduced in DirectX 11 (e.g. see http://forums.xna.com/forums/p/47758/286094.aspx#286094).

Other useful tidbits of information:

• A tool called GPU MeshMapper is provided by AMD for generating mapping from a low-poly mesh to a high-poly mesh that is appropriate for use with recent ATI Radeon graphics cards.
• AMD developed a hardware tesellator plug-in for Autodesk Maya that you can download at http://developer.amd.com/gpu/wgsdk/Pages/default.aspx.