There is one king. All of the other pieces revolve around him and their entire mission is to protect and serve him. G-d is the King, all else was created by Him, given the opportunity to connect to His truth and to serve Him.
The queen is the feminine manifestation of the divine, known as the "shechinah," intimately involved with every aspect of creation, granting vitality and substance to every existence. The queen is the most practically affective piece, often sent into the lines of fire, even placed in danger. Likewise, G-d risks His own dignity, as it were, by investing Himself in every creature and existence, subjecting Himself to the vicissitudes of the human condition.
Then there are bishops, rooks, and knights. They are swift, free, not limited by the squares immediately surrounding them; they can "fly" around freely, without constraints. These are symbolic of the angels-in their three mystical categories we discuss in the daily morning services, "seraphim," "chayos" and "ofanim," represented by the bishops, rooks, and knights.
In order for there to be free choice in the world, there are two teams, the white and the black. One team representing G-dliness and holiness; the other team representing everything antithetical to G-dliness and holiness. The teams are engaged in fierce battle. And for the confrontation to be meaningful each team contains, at least on the surface, all the properties contained in the opposite team. Both teams pretend to have a king, queen, bishops, rooks and knights.
Finally, there are the pawns. They are very limited in their travel, moving only one step at a time, only in a singular direction, and they constantly get "knocked off." But... when they fight through the "board," arriving at their destination, they can be promoted even to the rank of the queen, something that the bishop, rook or knight can never achieve.
The Pawn represents the human being living down here on earth. We humans take very small steps, and we are so limited in every aspect of our journey and our growth. We also constantly make mistakes and get "knocked down." But when man perseveres, and overcomes the angst and despair of his or her own failings and mortality, when we fight the fight to subdue darkness and to reveal the presence of the "king" within our own bodies, our own psyches and the world around us-the human being surpasses even angels; the pawn is transformed into a queen! The human life reunites with its source above, the queen, the Shechinah, experiencing the deepest intimacy with the King Himself.
The bishops, rooks, and knights, though spiritually powerful and angelic, are predictable, and limited by their role. There is no room for real promotion, no substantive growth, no radical progression. Yes, they fly around, but only within their own orbit. The angels on high, as well as the soul alone on high, before entering the body, are powerful yet confined by their own spiritual standing. It is the limitations of the human person that stimulate his or her deepest growth. The limits of our existence create friction, causing us to strain against the trials and disappointments of life.