Similar to dropping a deuce, which means to move your bowels; dropping 20s means the same thing, the only difference is that it is 10 times worse. Explosive diarrhea could be considered a 20.
"Hey John, I really gotta go drop this 20."
"Huh? Drop a 20?" replies Stan.
"Yeah my dude, I feel like I gotta drop 10 deuces so make way!!!!"
"Oh I get it, dropping 20s." chuckles Stan.