This is a tradition that started in Russia. Its the 256th day of the year; if you dont get the joke then its not your day.
By chance Im in Tomsk at the moment with our Russian development team. So today we are going to celebrate by going out to lunch.
Ive always loved this idea. Ive even registered the relevant domain with a view to making it a thing at some point. The reality though is that Im running a software company and dont have much spare time to do this. If anyone is interested in getting involved with making Overflow Day more popular across the globe please get in contact.
In Russia today is known as the Day of the Programmer. I prefer to highlight the joke, so go with Overflow Day. Also, there are so many roles in IT beyond programming testing, UX, etc I prefer the more inclusive form; if you get the joke, its your day.
More info on Wikipedia https://en.wikipedia.org/wiki/Day_of_the_Programmer