Despite claims this phrase originated on "The Simpsons", it actually existed long before it was used in the show. The phrase is intended to portray the distortion of facts when passed from person to person.
Its use in "The Simpsons" was accurate; Bart starts a rumour by whispering to one person who whispers it to another, etc. By the time the rumour reaches the front of the crowd, the phrase "Purple monkey dishwasher" has been added to the end due to people mishearing the original rumour as it passed from person to person.
Due to the popularity of "The Simpsons", the phrase has since become a commonly used response to opinions stated based on hearsay and unconfirmed rumours.
Person A - "I heard from a friend of a friend that John cheated on Linda with Karen!"
A parody of the game 'telephone' used on an episode of The Simpsons. Instead of an original message becoming jumbled by person to person contact, the message is perfectly repeated at the end...but with the addition of the words "purple monkey dishwasher."
Nora's pregnant with Greg's baby after sleeping firt with Tony, John and Barney...but she's telling Tim it's his due to their fling at Thanksgiving....purple monkey dishwasher.
A nonsense phrase seen widely in an early Simpson's episode. Added at the end of a Chinese whisper, ironically, as there are few if any phrases which can be mistaken for "purple monkey dishwasher". For this reason, it is sometimes used to check if communications are working properly, instead of ie. "testing" "mic check" "testtest 1 2 3 check" and/or "syphilis".
Originating from an episode of the Simpsons (episode 2F19 "The PTA Disbands")
It has taken on a comical nonsensical interjectional use... appropriate as comic relief or as a tension breaker