The Collaborative International Dictionary of English v.0.48:

millennium bug \mil*len"ni*um bug`\ (m[i^]l*l[e^]n"n[i^]*[u^]m
   b[u^]g`), n. (Computers)
   An error in the coding of certain computer programs which
   store the year component of the date as two digits, assuming
   that the first two digits are 19, rather than as a complete
   number of four digits; when such programs are used after
   January 1, 2000, the date may be misinterpreted, causing
   serious errors or total failure of the program; -- called
   also year 2000 bug, year 2000 problem and Y2K bug.

   Note: In the several years leading up to the year 2000, large
         corporations and other users of computers in total
         spent many billions of dollars correcting this error in
         the programs they use.
         [PJC]

The Collaborative International Dictionary of English v.0.48:

year 2000 bug \year 2000 bug\, year 2000 problem \year 2000
problem\, n. (Computers)
   an error in the coding of certain computer programs in which
   the year portion of dates was represented by only two decimal
   digits, assuming that the first two digits are "19". In such
   a program the the year 1975 is represented as "75". This was
   a common practise in computer programming even into the
   1990's, as many programmers failed to consider that their
   programs would be used after the year 1999. Thus, with such a
   program, a person born in 2000 would be considered as 101
   years old in 2001; many different serious problems, as
   various as the programs, could be caused by such an error.

   Note: In 1998 many programs with the year 2000 bug were still
         not corrected, and it is not clear how many programs
         will retain the bug when the year 2000 arrives. Tune in
         then.

   Syn: millemium bug, Y2K bug, Y2K problem. [PJC]