The truth is that the phrase �a square meal' is a relatively recent creation. It originated amongst 19th century hoteliers in the USA. as an advertising gimmick. The word �square', in this sense, means honest, fair or satisfactory, just as it does in a �square deal'.
It has nothing to do with the shape of the thing it was served on. Some claim it relates to a square tray that sailors supposedly used to have their food served on, but that is not the case either.
I thought it was the portion of food dished up on the 15/16 century ships. A square wood board with a rim round the edge, so everyone got the same portion.