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 Free On-line Dictionary of Computing (30 December 2018):

Year 2000
century meltdown
millennium bug
millennium meltdown
Y2K

    (Y2K, or "millennium bug") A common name for all
   the difficulties the turn of the century, or dates in general,
   bring to computer users.

   Back in the 1970s and 1980s, the turn of the century looked so
   remote and memory/disk was so expensive that most programs
   stored only the last two digits of the year.  These produce
   surprising results when dealing with dates after 1999.  They
   may believe that 1 January 2000 is before 31 December 1999
   (00<99), they may miscalculate the day of week, etc.  Some
   programs used the year 99 as a special marker; there are
   rumours that some car insurance policies were cancelled
   because a year of 99 was used to mark deleted records.

   Complete testing of date-dependent code is virtually
   impossible, especially where the system under test relies on
   other systems such as customers' or suppliers' computers.
   Despite this, the predicted "millennium meltdown" never
   occurred.  Various fixes and work-arounds were successfully
   applied, e.g. time shifting.

   And yes, the year 2000 was a leap year (multiples of 100
   aren't leap years unless they're also multiples of 400).

   PPR Corp Y2K FAQ
   (http://pprcorp.com/y2k/y2kfaq_j97.html).

   (2003-08-15)