Exactly what it sounds like.
Don't shower or shave on Sundays. Take this day for yourself. Enjoy yourself without worrying about what other people think. Who cares if you smell bad and look unkempt, its about showing the world you don't care. (at least you don't care once a week)
Bob: "Dude, you smell terrible."
Joe: "Yea I didn't shower or shave today, its No Shower No Shave Sundays"
Bob: "Oh yea I forgot, then nevermind, you smell terrible, but you are SO cool for not showering and not shaving on Sundays. How can I be cool like you?"
Joe: "Step one: Don't shower on Sundays. Step two: Don't shave on Sundays"
Bob: "Sounds like a plan, homeskillet!"
Joe:"Step three: NEVER say homeskillet again."