Back in the dark ages of computer technology, memory was very expensive. To save space, PC programmers coded computer hardware and software to accept input of the last two digits of a year; the system would then automatically place a `19' in front of the digits.
Next year, when the PC (or its mainframe, or microchip) starts getting input that reads `00', it will interpret the data to mean the year 1900. Surprise! Suddenly, you haven't been born yet. Worse, your bank account hasn't been born yet, and the IRS is calling because you haven't paid taxes in 50 years.
Any business that relies on computers (with the exception of all you Mac users out there!) could go haywire if its hardware and software can't process millennium data correctly.