Microsoft was the first to release their "next generation" console before Sony or Nintendo got a chance. What consumers got was a console much more powerful than the original Xbox, high definition output and the chance to play HD-DVD movies (with a seperate HD-DVD drive). By the time Sony launched the Playstation 3 the Xbox 360 was already in many people's homes.
Although not as powerful as its nemesis (Sony's Playstation 3) it provides a great platform for network games and has a wide range of games, admittedly mostly aimed at Western males, but wide nonetheless. It specialises in First-Person Shooters and Driving games.
The Xbox 360 is available in two main versions - Arcade and Elite. Arcade is the most basic model, you get very little with the package (and a tiny harddrive that will prevent you using most online content) but it's very very cheap. Elite gives you the whole package, including a large hard drive but is more expensive.