@Nancy88,
Y2K = year 2K = year 2000 = the year 2000.
(K = 1,000.)
Y2K as a term refers specifically to fears people had about 1999 changing over to 2000. There were worries about computers all going haywire simultaneously and implications thereof. (I forget exact details but it was something about how computers would think it was 1900 rather than 2000 -- because only the last two digits of a year date mattered -- and how that would mess everything up.)
People who were worried about very bad things happening at 12:01 AM January 1st, 2000, did things like stock up on everything they could get their hands on ahead of time. (Items like toilet paper.) There were a lot of bare shelves on December 31st, 1999.