In past years, before the astronomic increase in computer memory that we have today, computer programmers had to conserve as much memory as possible. One of the ways this was done was to use 2 numbers in the year field instead of the entire 4 number date.
 What this means is that on January 1st, 2000, every  computer in the world that's not Y2K compliant will roll over from December 31, 1999 to January 1, 1900.
We've known since 1754 (when England and by extension, her colonies in America, adopted the Gregorian calendar) exactly when the millenium was going to be, and we've known for about 3 decades that this was going to be a problem, but in true human fashion we only started working on this very, very recently.

The ramifications of this could be earth shaking.
For more information see these sites, and follow the links on them to still others.

http://www.y2k-status.org/

http://2000andyou.com/2000/main.html