The day that people realize that all the drinking and partying they did the night prior to (as in
New Year's Eve) was worthless, because, in reality, it means nothing. The day of New Year's Eve is exactly the same as New Year's Day. It is also often used for people living crap lives to say all the things they are going to do "this new year", none of which they really will do, that end up being almost identical to
last year's.
The only true difference between New Year's Day and the day of New Year's Eve, is that when writing the date, you must change one, or more (depending on what year it changed to) digits in the year category. When in school this becomes a nuisance when teachers
deduct points due to writing the wrong date.