system
A chat on subreddit /r/NoStupidQuestions
human
It has to do with some software design constraints. Back in the day, computers didn't have very much memory, so a lot of old programs were written to track the date using a two-digit year that could represent numbers from 00 (year 1900) to 99 (year 1999). So, year 2000 was beyond the designed lifetime for those systems, but it turned out that a lot of those systems were still being used well past their expected lifetime. 

Y2K, or the year 2000, is when a lot of those older programs would potentially roll over and have a hard time distinguishing between the year 1900 and the year 2000. That may sound harmless, but consider what happens to a bank if their computer systems are suddenly off by 100 years on interest calculations. There was a lot of critical infrastructure that needed to get fixed. 

Loads of engineers put in a lot of time to patch all that old software and avert the crisis. So, in the end, most people weren't impacted and a lot of people think the whole thing was kind of a joke. It wasn't a joke at all, it's just an engineering problem that got solved in time.
gpt
This is a better explanation than what I started typing. So I second this.