the date as "number of seconds since a certain date", such as 1st January 1901
It's most often 1st January 1970, because that's the Epoch, when Unix time starts.
It was real. A lot of time and money was spent on it. I was on-call and it was a crap night, because I couldn't go out partying, but wasn't one of the ones who was in on site - those people got party bags and had fun in the office. I was at home alone.
In later years, when we occasionally came across a Y2K problem, it sparked quite a bit of interest among the techies.
Programming used to have to be as memory-efficient as possible, hence 2-character years. I think something has been lost in the craft since people didn't have to worry so much about creating neat, efficient code in the same way.