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1.
After having rough sex, the dude pops his red balls (resembling elmo) into the chick's ass, thus making it dirty. Afterwards, the chick can either lick it off, like a lollipop, or just enjoy the ball to anus pleasure. The definition is quite flexible.
Example 1 (balls into anus):
Dude1: Dude, she's so hot.
Dude2: I'm gonna enjoy poppin the dirty elmo.

Example 2 (lollipop licking the dirty elmo):
Dude1: Dude, I hear she's quite rough in bed.
Dude2: I hope she enjoys poppin the dirty elmo.
by Captain Elmo April 01, 2005