Short for "year 2000". Also known as the "Y2K scare" or "Y2K bug".
Since computers only counted the last two digits in a number (e.g. 1984 would be 84), they would reset 1/1/2000 to 1/1/1900. This lead to everyone thinking all of the computers would crash since the PC's wouldn't know what the date was and all the information would be lost forever.
People worried about their money, jobs, houses, loans, all that jazz. We all went berserk and thought we were gonna go back into "caveman times". However, it didn't happen.