The King, Queen and Bishop
The king and queen obviously represent the monarchy that ruled over most aspects of Medieval life. As such, the king is the most important piece in the game (though the queen is the most powerful and versatile). The bishops represent the Church, the other center of power in the Medieval world. Appropriately, they sit at the right and left of the king and queen, as did many princes of the Church during Medieval times.
The Knight and Rook
The knight is fairly self-explanatory. It represents the armored aristocratic soldiers from the Middle Ages that rode on horseback. Rooks represent the castles knights often owned or defended.
Pawns
Pawns, the weakest pieces with the largest numbers on the board, represent Medieval serfs. These were the indebted peasants upon whose backs much of the commerce and wealth in Medieval times was built.