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.
A trip to a grocery store, convenience store, or gas station for the sole purpose of buying an excessive amount of junk food and sugary drinks, usually with friends. A chud run often happens late at night and ends with everyone involved hating themselves afterwards.