When you need to take a long, satisfying pee you've been holding onto for a long time.
Please note, a monstrous piss is one of the only 2 types of pisses, the other being the 'insurance piss.'
Guy: "Heyo, I see a restroom over there. Hold on, I gotta take a monstrous piss"
Other guy: "Good call, I could use an insurance piss anyway."