drink
First let us break down the meaning of the word by defining the Kanji (Borrowed Chinese Characters).

新 = New

年 = Year

会 = Meet or Party

As with the Bounenkai (忘年会), Shinnenkai’s are pretty much the same. Meet with your friends, colleagues, clubs, teammates,etc. Drink, eat and be marry is the best way to describe it. Also expect to go out after the first party to the “second party” and “third party”.

2nd Party = 二次会　＝ Ni Ji Kai

3rd Party =　三次会 = San Ji Kai

4th Party = 四次会 = Yo Ji Kai

5th Party = 五次会 = Go Ji Kai

Don’t forget that most likely you will be hung over so take off the next day.

Hang Over = 二日酔い = 　Fu Tsu Ka Yoi