It is a fun word for toilet, restroom. It is a place where you can do number one and number two. It rhymes with bipiti baapti, the American version of how Italians speak. A short form of Peepary-Poopary is poopary, if you feel it's too long, but it's always fun to say it fully and I recommend it to experience the complete effect of the word. It is allowed to use the world as poopary-peepary.
Sean: Where is James?
Joe: He's been in the Peepary-Poopary for more than an hour.
Sean: Speaking of which, I need to make a quick visit to the peepary-poopary myself. I hope James finishes soon.
It is a state wherein one feels the urge to drop his load but at the same time, it just won't happen even after trying hard.
Felef: you know thatfeeling you feel like you're gonna poop but also feel like you won't?
Hark: Lol torment! Looks like you're stuck on poopgatory! give it some time man.
Upon finishing your business in the bathroom, you realize there's no toilet paper. You're stuck with shitty butt until someone arrives with toilet paper redemption.