Symbols are objects, characters, figures, and colors used to represent abstract ideas or concepts.
The tempest that begins the play, and which puts all of Prospero’s enemies at his disposal, symbolizes the suffering Prospero endured, and which he wants to inflict on others. All of those shipwrecked are put at the mercy of the sea, just as Prospero and his infant daughter were twelve years ago, when some loyal friends helped them out to sea in a ragged little boat (see I.ii.144–151). Prospero must make his enemies suffer as he has suffered so that they will learn from their suffering, as he has from his. The tempest is also a symbol of Prospero’s magic, and of the frightening, potentially malevolent side of his power.
The object of chess is to capture the king. That, at the simplest level, is the symbolic significance of Prospero revealing Ferdinand and Miranda playing chess in the final scene. Prospero has caught the king—Alonso—and reprimanded him for his treachery. In doing so, Prospero has married Alonso’s son to his own daughter without the king’s knowledge, a deft political maneuver that assures Alonso’s support because Alonso will have no interest in upsetting a dukedom to which his own son is heir. This is the final move in Prospero’s plot, which began with the tempest. He has maneuvered the different passengers of Alonso’s ship around the island with the skill of a great chess player.
Caught up in their game, Miranda and Ferdinand also symbolize something ominous about Prospero’s power. They do not even notice the others staring at them for a few lines. “Sweet lord, you play me false,” Miranda says, and Ferdinand assures her that he “would not for the world” do so (V.i.174–176). The theatrical tableau is almost too perfect: Ferdinand and Miranda, suddenly and unexpectedly revealed behind a curtain, playing chess and talking gently of love and faith, seem entirely removed from the world around them. Though he has promised to relinquish his magic, Prospero still seems to see his daughter as a mere pawn in his game.
Like the tempest, Prospero’s books are a symbol of his power. “Remember / First to possess his books,” Caliban says to Stephano and Trinculo, “for without them / He’s but a sot” (III.ii.86–88). The books are also, however, a symbol of Prospero’s dangerous desire to withdraw entirely from the world. It was his devotion to study that put him at the mercy of his ambitious brother, and it is this same devotion to study that has made him content to raise Miranda in isolation. Yet, Miranda’s isolation has made her ignorant of where she came from (see I.ii.33–36), and Prospero’s own isolation provides him with little company. In order to return to the world where his knowledge means something more than power, Prospero must let go of his magic.