I shall stoop down to fanboy level in explaining the tesselator:
Its amazing innit! Basically reet, it does this cool stuff where it adds detail to the scene. It makes it amazingly uber cool, better than all the other cards innit! OMFG this is soooo amazing!!!1111oneonetwo I was like no way!?! But it did it, omg I can't believe it did it!
Now for the people who actually want to know what it does:
It performs a complicated analysis from a surface (however, I wouldn't be surprised if there were numerous weights a game dev can apply, maybe even sending the original heightmap to the driver), and then adds vertices where there were none before. In essence the terrain can become extremely detailed with no extra work being performed by the CPU, or the game devs.
Now - you could just send over a high detail mesh, but you would quickly bottleneck the PCI-E bus. Additionally you wouldn't have *that* much control over LOD since shaders won't increase performance anywhere near as much as the tesselator. In essence you can have a LOT of vertices right in front of you and smoothly decrease the LOD as the terrain gets further away. You don't have to worry about sending new meshes, performing LOD on the CPU, etc. etc. Its a very cool feature, and a primary reason why you can get very large highly detailed outdoor scenes on the Xbox 360 (think Kameo).
Since it uses a dedicated unit, all these calculations have no impact on shader performance, actually quite the reverse.