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