The Xbox 360 Elite is the third version of the Xbox released, and it included several new features. (Listed below)
Features
120GB hard drive, which is about $30 extra for a comparable PC part.
Black matte cover. (Note: It's not glossy like the picture above)
Includes a black controller.
Includes an HDMI cable, which goes to up to 1080p, currently the highest resolution available. (The best you could go up to to with the component interface was 1080i)
Some versions come with 2 games from 2006; Forza Motorsport 2 and Ultimate Alliance. Note: They used to ship with a 360 Arcade.
A load of demos, and one full game. (A puzzle game called Hex, woo-hoo)
(From my experiences), it doesn't overheat nearly as much. Which is still all the time.
Most, if not all, of the main features the Xbox 360 Premuim version had.
Basically just a 360 Arcade, just Microsoft gets to stiff you for another $150 bucks.