Fance-O-Dance was the name of the automatic mechanical dancing shoes that Doctor Emmett Brown designed in the 1940s.
In 1945, the blueprints for the shoes were destroyed in a building fire. When Doc Brown demonstrated the shoes for his son, Verne in 1992, they burned out, and Doc couldn't fix them without the blueprints. So, Marty McFly snd Verne travel bsck to September 27, 1944 to retrieve the blueprints from Doc's apartment.