I understand why there would be a king and queen but I would love to know where the idea to call pieces what they are - such as the Rook, Knight, Bishop and Pawn - came from. Is there any background information on the reasons they were called this, and why they were assigned their specific move set?
I believe that the chess pieces are supposed to constitute an army - I'll try to give a breakdown of how each individual name evolved.
Xianqi, or Chinese Chess, originally developed in India before spreading across the world. Xianqi is the Chinese interpretation of the ancient game, and the pieces do really sound like those that would be in an army - General, Advisor, Cannon, Elephant, Horses, Soldiers, and Chariots.
When the game moved to Persia, as referenced by user Akavall in the comments, the Persian word for chariot is "rokh" and is naturally what the piece is called today.
The modern interpretation of chess holds its roots in Spain where one of the final transformations occurred. The General piece became the King and the Advisor became the Queen, as these positions were more familiar in the Western environment. The horses became knights and the elephant became a bishop (I suppose this was influenced by the Church's power during this era). The Soldiers became known as pawns (from Anglo-French poun, or Old French peon).
If you want to read more about this, this link might do a better job explaining it than I did: How Did Chess Pieces Get Their Names?
Rook which is basically chariot is called Rath (hindi) or Ratha (Sanskrit) or Rukh (persian)
Mantri/Wazir which means key minister/counsellor, is todays queen.
Ghoda (hindi) and Ashva (sanskrit) means horse which is basically our modern Knight
Hathi which means elephant is our modern bishop
And finally pawn was called Padati, nowadays called Paida (hindi) in short.
According to this article, it went to china much later...