To make sure that the surface is clear from any previous application residue or any dust/dirt that may have statically attracted itself to the car between stages.

If you QD a car between all stages, then it minimises the risk of imperfections (scratches, swirls, etc...). A prime example is with the "sealer" stage. If you have any polish residue, a sealer (like AG Extra Gloss) will seal these in until it physically wears off. Same with the wax. If there is some sealer residue that has been missed, a wax will go over it and possibly "react" or smear. A wipe over with QD will remove any of this. Think of it as a panel wipe that you would use if you were painting.

Even when simply washing a car, if you live in a hard-water area, wash the car and then either spray a light mist of QD over the car before drying (acts as a water repellant) or QD once dried to remove water marks.