From the original description of the concept: nanotechnology is based on the concept of tiny, self-replicating robots. The utility fog is a very simple extension of the idea: suppose, instead of building the object you want atom by atom, the tiny robots linked their arms together to form a solid mass in the shape of the object you wanted? Then, when you got tired of that avant-garde coffee table, the robots could simply shift around a little and you'd have an elegant Queen Anne piece instead.