Y2K literally means "Year 2000". Here is what wikipedia has to say:
"The Year 2000 problem (also known as the Y2K problem, the millennium bug, the Y2K bug, or simply Y2K) was a problem for both digital (computer-related) and non-digital documentation and data storage situations which resulted from the practice of abbreviating a four-digit year to two digits.
In computer programs, the practice of representing the year with two digits becomes problematic with logical error(s) arising upon "rollover" from x99 to x00. This has caused some date-related processing to operate incorrectly for dates and times on and after January 1, 2000 and on other critical dates which were billed "event horizons". Without corrective action, it was suggested that long-working systems would break down when the "...97, 98, 99, 00..." ascending numbering assumption suddenly became invalid. Companies and organizations worldwide checked, fixed, and upgraded their computer systems.
While no globally significant computer failures occurred when the clocks rolled over into 2000, preparation for the Y2K problem had a significant effect on the computer industry. There were plenty of Y2K problems, and that none of the glitches caused major incidents is seen as vindication of the Y2K preparation. However, some questioned whether the absence of computer failures was the result of the preparation undertaken or whether the significance of the problem had been overstated.
Many banks have responded to the Y2K problem by forcing full 4-digit year entries on cheques, which helps to prevent the error from occurring in accounting environments."