However, prior to the adoption of the Julian Calendar, New Year's Eve was in March.
In other calendar systems a "new year's eve" would necessarily fall on the date those calendars called the beginning of the new year -- like Tet in Viet Nam or the Chinese New Year, based on lunar systems and thus a floating day by Western standards.
A hallmark of new year's celebrations in all cultures seems to be some sort of commemoration of the previous year's events, a sense of renewal, and a recommitment to a better next year. There are wide disparities in the forms and level of importance of each of these elements, and individual cultures must be examined for specifics.
In the United States New Year's Eve is a major social holiday. In the past 100 years the dropping of the 'ball' on top of 1 Times Square in New York City, broadcast nationwide, is a major component of the celebration. Drinking champagne is also a major part.
For about four decades Guy Lombardo and his Royal Canadians would serenade the nation from the ballroom of the Waldorf Astoria on Park Ave in New York. But every city in America has its own local version of the celebration, even while keeping and eye on New York, and the New York-centric aspect of the holiday is diminishing.
Within many cultures the use of fireworks and other noise making is a major part of the celebration.
Within Western Cultures at least, but some others too, there is an idea of making "resolutions" -- or commitments to do better next year -- on New Year's Eve.
Most New Year's Eves have passed with just festivities. The major exception in current times was Y2K.
However, what we could style as Y1K -- 999 changing to 1000 -- saw a great religious importance in Christianity because of the expected rebirth of Jesus. Though ignored for a long time, this aspect of that historical period is getting more attention as of late.