A poop that requires no toilet paper afterwards due to the fact that it left nothing behind on your behind.
Dude, I was just taking a shit and realized there was no toilet paper. Luckily it was a birthday dump, or I would have been in big trouble.
You are hammered drunk and you decide to drop one down, only you find that it happens to be the best damn turd of your young life. It was so good in fact, that you feel as if it was your birthday.
On occasion, the loaf itself refuses to be flushed, enhancing/dampening the birthday effect depending on location.
You are wishing someone happy birthday at a bar, perhaps for their 12:01, and instead of singing the happy birthday song when everyone else is singing it, you yell "take a birthday dump....Jesse Reimer!"
"TAKE A BIRFDAY DUMP" (if ur black)