Referring to the quick step dance move seemingly taken on by people who have to run to the bathroom with explosive diarrhea. Here say suggests that green apples can induce such a predicament - hence the moniker.
This is popular slang in the medical community when referring to patients who have such a reaction to medication such as lactulose given to patients with liver disease.
In popular culture, this was also the name of a 90's grunge band from Seattle.
Dr. Jason prescribed lactulose to Steve who promptly did the Green Apple Quick Step making it to the bathroom with a photo finish.