From Tommo, MIDN, RAN, Royal Australian Navy: Another Naval expression, correctly described by the second person as being to efficiently fit more plates on a sailors' table. A square plate allowed a larger amount of foot on a relatively smaller plate. So a square meal was a larger meal than they would otherwise be having - a good square meal being a favourable thing.
Tables only had one finished side. The other side, less expensive to make, was more rough. When the family was alone, they ate on the rough side to keep the good side nice for company. When company came, the whole top lifted off and was turned to its good side.