Don’t know. I found this graphic on Engadget, but it appears they replaced it with a newer, slightly LESS appropriate image. Odd.
Basically, Microsoft thought it wise to name the new Xbox as Xbox 360… however, I thought it was a stupid name, and if they had only named it Xbox 180 it would have fit better. Sorta like, “Microsoft is doing a 180 on the Xbox design” or some such nonsense.

Not that I hate Microsoft, but somehow this just fits.
Update: Just to clarify, Engadget NEVER used the 180 graphic. Perhaps had I worded it differently, it may have appeared as satire.
Update: Just changed the link to a static Flickr version.
They named it xbox 360 because of xbox live. The world has360 degrees and people around the world can play on xbox live which is why they named it xbox360.