What are “three piece moves” all about ? Why are they most difficult?

Three piece moves are the most difficult because they are the heaviest... the most "burdensome" and difficult.

Even after the moves where we only moved three pieces—especially after the three-piece moves, actually—the gratification would still be there. Three-piece moves were always the most burdensome, particularly since two or three would typically be assigned in one day. Nobody called Fast Company to move a few pieces unless those pieces were massive: ten-foot, two-piece bookshelves, fireproof file cabinets, safes, pianos, and armoires.