Who is Ariel?

Ariel is a spirit of the air in Shakespeare's The Tempest. When the banished Prospero first arrives on his island exile, he discovers that Ariel has been imprisoned in a pine tree by the evil witch Sycorax. Prospero frees Ariel, for which the little spirit is immensely grateful, as one can well imagine. As an expression of gratitude, Ariel becomes Prospero's loyal and faithful servant. Like his new master, Ariel has magical powers, which he proceeds to use in accordance with Prospero's wishes. For instance, it is Ariel who whips up the storm—the tempest of the play's title—which causes the King of Naples and his crew to become shipwrecked on the island.
When Prospero frees Ariel from his imprisonment in the pine tree, he promises that he will one day give him his freedom. In the meantime, however, Ariel remains as Prospero's servant. Although Prospero treats Ariel a good deal better than Caliban—which isn't really saying all that much—he never lets him forget who's boss, even threatening at one point to imprison him for twelve years in an oak tree if he doesn't stop complaining:

If thou more murmur’st, I will rend an oak And peg thee in his knotty entrails till Thou hast howled away twelve winters (act 1, scene 2).

Despite, or because of, Prospero's bullying behavior, Ariel continues to serve his master diligently, but it's only when he impresses Prospero that he is finally released. This happens after Ariel uses his magic powers to make Ferdinand and Miranda fall in love. The forthcoming nuptials between his daughter and Ferdinand mean that Prospero can now return home to Milan. As he has no further need of Ariel's services, he makes good on his promise to give Ariel his freedom.