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Prospero asks about King Alonso and his attendants. Ariel informs his master that the shipwrecked group is a pitiful sight: the three traitors (Alonso, Antonio, and Sebastian) are distracted and the rest are mourning. Ariel says Prospero's feelings toward the group would become tender at the sight and Ariel would cry... if he were human.
Hearing Ariel speak so kindly, with mercy befitting a human, Prospero says he'll put his thirst for vengeance aside and be merciful. He sends Ariel to free the traitors and the rest of their crew from their confusion, and draws a magic circle with his staff (his big magical stick).
As Ariel leaves him, Prospero muses on all that he has done with his potent art of magic, and solemnly says that once this last task is done, he'll break his staff and bury it in the earth, and drown his book in the ocean. In other words, the guy is giving up his magic.
Ariel arrives, dragging behind him a frantic Alonso, Gonzalo, Sebastian, and Antonio, with their attendant lords Adrian and Francisco. They all stand in Prospero's magic circle, charmed, as Prospero addresses each of them.
He speaks to Gonzalo first, and tears up as he thanks him for being his "true preserver" and remaining so loyal to whomever he serves.
Prospero then chides King Alonso for treating him and Miranda so poorly, and says Sebastian, too, suffers for wronging them.
Finally, Prospero comes to his terrible brother Antonio. Prospero reveals that Antonio plotted with Sebastian to murder the King, but forgives them all.
Prospero then notes that the group may not recognize him (which is kind of a bummer, as they don't know how gracious he's being, given how bad they were to him). Prospero then asks Ariel to bring his hat and sword, so they might know that the man before them is the old, genuine Duke of Milan.
As Ariel dresses Prospero, the airy spirit sings another pretty little song and Prospero notes, though he will miss Ariel, the spirit will surely soon have his freedom. All Ariel needs to do is bring the sleeping mariners (remember them?) from their ship to this spot.
Alonso and all the shipwrecked gang look on, unsure whether this is more enchantment, or if it's really Prospero before them. Alonso, struck, immediately returns Prospero's dukedom and asks for Prospero's forgiveness. Alonso also wants to know how Prospero survived and ended up on this island. (Did he tie together a fleet of sea turtles? Build a raft out of human bones?)
Prospero turns then to Gonzalo, praising him again before getting back to Antonio and Sebastian.
Prospero says he could say some things that would raise a couple of eyebrows, but out of the kindness of his heart, he will keep them to himself. The pair of traitors is not even a bit ashamed or sorry. Sebastian claims the Devil speaks in Prospero, but Prospero ignores this, and instead wholeheartedly forgives his traitorous brother Antonio.
King Alonso brings up the loss of his son, Ferdinand, and Prospero cryptically says he has lost his daughter—they've lost both children on account of the tempest. The story of how all of this came to be, he says, is not the kind of thing that can be discussed over a single sitting, but over the course of long days. In the meantime, they can entertain themselves with other things.
Perhaps, for instance, they'd like to take a look in Prospero's humble cell?
Prospero draws back the curtain to his home and reveals Ferdinand and Miranda, who happen to be playing chess. (That's not a euphemism.)
Alonso and Ferdinand are pleasantly surprised to find each other alive, and Miranda, faced with so many dudes for the first time, declares "O, wonder! / How many goodly creatures are there here! / How beauteous mankind is! O brave new world / That has such people in't!" (The writer Aldous Huxley liked this so much that he chose the phrase "brave new world" as the title of his famous book.)
Alonso points out that Ferdinand can't have known the girl he's playing chess with for more than three hours, but hears the surprising news that the girl is his new daughter-in-law, three hours or no.
Gonzalo, Alonso, and all the other "good" guys are overjoyed with the news.
Ariel then enters on cue with the boatswain from the first scene, who happily announces that not only are all the sailors alive, but the ship is good as new. Like magic.
Alonso, meanwhile, thinks they should consult an oracle about how on earth all of this very strange stuff has happened, but Prospero tells him to relax. He assures Alonso that he'll explain everything eventually, and for now they should just enjoy the moment.
Finally, Prospero tells Ariel to free Caliban and his companions from the whole "being savagely hunted by hounds" spell. Stefano, Trinculo, and Caliban enter, the former two in Prospero's stolen clothes.
Alonso claims Stefano as his drunken butler, and Prospero claims Caliban as his own slave-begotten-of-a-witch-and-the-Devil. There's some punning on being in a pickle, and Prospero, in a merciful mood, demands that Caliban take his friends and go to work tidying up the cell, if he wants forgiveness.
Caliban relents that he was, as we suspected, a "thrice-double ass" to take this drunkard Stefano for a god. The three exit to prepare Prospero's cell.
Prospero invites Alonso and everyone back to his place, where they'll be treated to Prospero's long life story.
Prospero promises that in the morning they'll all go on the newly fixed ship to Naples. Once there, Prospero hopes to see the children married, and then head back to Milan, "where every third thought shall be my grave."
Alonso glosses over this happy little sentiment by saying he looks forward to Prospero's autobiography.
Prospero promises tomorrow will bring them favorable weather (and no more tempests!). He leaves Ariel the final task (yes, this is like, his sixth final task) of seeing to the weather, and after that the spirit is finally free.
Prospero sends everyone into his home, and then speaks directly to the audience.
In the play's final speech, Prospero informs the audience that the only thing that can free him from the island prison and send him to Naples is the audience's applause and approval.
P.S. Some literary critics think that this speech is Shakespeare the playwright's way of saying "so long" to the theater. If you want to know more about this, go to "Symbolism."