If I understand your question correctly, magic is used extensively throughout "The Tempest" and is one of the major themes of the play. Some scholars believe the magic of Prospero relates to Shakespeare's own personal "magic" with writing for the stage, and the idea of illusion vs. reality is important to the play as well as to theater audiences who must suspend their own disbelief to enjoy the performances.
When Prospero took over the island, he learned and used magic to control its inhabitants like Caliban and Ariel. And we continue to see his use of magic throughout the play, until finally, at the end, when he will be able to return to Milan, he gives up all of his powers and has forgiven his enemies:
"I'll break my staff,
Bury it certain fathoms in the earth,
And deeper than did ever plummet sound
I'll drown my book." (5.1)
Check the links below for more information, especially the link to "themes" of the play. Good luck!