The remainder of a smoked joint that is much larger than the average "roach" and has been disposed of, on the ground, by a smoker who has had reason to dispose of it. A "papa roach" is minimum one-third of a full joint. Papa roaches are often found at the initiation site of a police chase as the person smoking the joint may likely attempt to dispose of the "evidence" by throwing the partially smoked joint out the window of a car.
Korey - "Hey man, did you see that guy take off in his 1995 Ford Escort?"
Bennett - "Yeah, lets go check and see if he tossed a papa roach."
Like many bands out there, catchy music but I cringe at their lyrics (when I happen to think on them). Popular enough for me to want to buy an album and place it near the back of my CD folder.