An off day, also referred to as a bad day (and not to be confused with a day off), is a day where you're...not yourself. Maybe you've been a bit down on your luck as of late. Maybe your parents are reminiscing to their friends about that awful/embarrassing thing you did when you were four years old that you've been trying to forget for at least a decade or two. Whatever it is, you're probably going to be very sullen until your life starts showing improvement.
My mate suffers from depression, and he has both good days and off days. One day he'll be just fine -- maybe even a little cheerful if something good has happened -- and then the next day, he'll be very sullen and down in the dumps; when this happens, there's absolutely nothing that can make the metaphorical rain cloud above his head disappear. You just have to wait until the off day runs its course.
In today's world, anyone can make up a holiday (i.e., Kwanzaa).
It has thus been declared that from this day on, April 2 will be known as National Jerk Off Day. Males of all ages should beat off on this day to their dick’s content! (Just because they can)