Dwight and Michael's Laundry Agreement refers to the deal struck by Michael for Dwight to do his laundry for a year after his betrayal in The Coup.
Dwight is convinced by Angela to contact Jan behind Michael's back in an attempt to become Regional Manager of the Scranton Branch. Michael suspects Dwight of such actions after receiving a call from Jan saying that a company employee had approached her saying that they could run the branch better. Upon being interrogated by Michael, Dwight offers to do anything for Michael, including his laundry, to which he agrees to do his laundry for a year.
During Travelling Salesman, Michael tosses his laundry to Dwight in the parking lot when leaving for a sales visit. Andy, who is accompanying Michael on the visit, asks why Dwight does his laundry, to which Michael responds "long story". On the subsequent car trip, he reveals that Dwight betrayed him, which then becomes the core of Andy's argument for Dwight to be fired.