Working in Japan is synonymous with enkai for many. Enkai are parties held for and by the employees of schools and companies.
Generally, a few times throughout the year, teachers will be asked to participate in an enkai after work. This usually involves dinner, speeches, sometimes games, drinking, and karaoke. Some enkai are overnight (usually optionally).
Enkai can be expensive but they can also be a good way to build relationships and get to know your coworkers better. Many personalities that don't show at work shine through at enkai.
Although enkai largely go by Vegas rules (what happens at enkai stays at enkai), don't forget that your coworkers are still your coworkers - so try to stay somewhat respectable!
Also be aware that if you have an enkai the night of closing ceremonies, you may still be expected to go to work the next day if it's a weekday.
Enkai are a favorite part of the job for many ALTs and other teachers, but if you can't attend one just say so politely. Likewise, if you don't drink be sure to politely but firmly inform the others that you will only be drinking the tea.
It is considered proper for enkai attendees to pour drinks for each other, especially from the lower ranking members for the higher ranking ones. Foreigners often aren't expected to do so, but it's a very nice gesture if you choose to do so. This is also a great time to strike up conversation with the person you are serving.