Prospero has been badly wronged. His brother Antonio stole his kingdom with the help of Alonso, the king of Naples. Antonio also arranged for Prospero to be set out to sea with his young daughter Miranda in a leaky vessel, expecting the ship to sink and his two enemies to drown.
Years later, Prospero has his enemies in his grip. He has spirited them to his island and can use his magic to do whatever he wants to them to make them pay for betraying him and for trying to murder him and his daughter.
He has a change of heart at the very end, however, due to Ariel. Ariel reports to Prospero that he has his enemies gathered together and trapped in a grove of trees. Ariel also states that these enemies are so terrified and upset that Ariel feels sorry for them.
Ariel's words move Prospero. How, he wonders, can a spirit—mere air, as Ariel is—feel emotions of mercy and compassion? If Ariel can have such feelings, how can he, a human being, not?
Prospero suddenly rises to a new stature. He knows he has the power to do whatever he wants to his enemies. He can take the low road and avenge himsel—or he can take the high road and forgive them. He decides to opt for the rarer and more humane act: forgiveness. He knows they don't deserve it, but he decides to do it anyway because it is the right thing to do. He also decides to give up his magic.
Prospero has a transformation to a fuller humanity beyond what magic has been able to offer him when he is able to forgive and show mercy to the undeserving.