Hands stuff pops up all over the place in this play. Prospero takes Miranda's hand before he tells her of their true identity, and our first introduction to the Prince and King has them below deck, praying, with their hands clasped. Ariel invites Ferdinand to take hands (presumably Miranda's) as he leads him away from crying over his father's death. Miranda is offered Ferdinand's hand as a symbol of his faith to her and of their marriage. Prospero gives Miranda's hand in marriage to Ferdinand when he agrees to their union, and Alonso clasps all their hands together and raises them to the heavens when asking God's blessing on the new union. Finally, when Prospero gives his epilogue speech to the audience, he asks that they bring their hands together, supposedly in prayer forgiving him his failures, but really in applause to tell him that he's totally awesome.
So, hands mean prayer, truth, love, and applause. (By the way, did you know the origin of the handshake was to show the other person your goodwill by revealing that you had no concealed weapon in your hand? Well now you do.)
Of course, to stretch this thing out the way English professor-types do, the ultimate importance of the hand is that it is the source of the translation from the mind to the page, the seat of writing and so the palm of the play. This act of translating words beyond the page, of making them worthy of playing, is the best thing that Shakespeare could hope to do. As his plays were written to be acted, applause (the act of the audience's hands) was the playwright's only assurance that he hadn't sucked. This is especially significant if we think of The Tempest as Shakespeare's last play. After a long career, the man deserved a bit of the audience's indulgence, in the form of their clasped hands, providing the ultimate praise of his own hand's work.