Who was Ariel, and how did he come to be Prospero's servant?

Ariel is an airy sprite or spirit that Prospero finds on the deserted island. Ariel was too good-hearted to cooperate with the "blue-eyed hag," the sorceress Sycorax. In revenge, she trapped him inside a cloven pine for twelve years, then died. As the text explains:



Into a cloven pine, within which rift
Imprisoned thou didst painfully remain
A dozen years; within which space she died
And left thee there, where thou didst vent thy groans ...




Ariel becomes Prospero's slave (or servant) after Prospero frees the spirit from the cloven pine. Ariel is grateful to Prospero for freeing him and becomes a good, intelligent, and faithful slave. He has an affectionate relationship with Prospero and can anticipate his needs. When Ariel asks Prospero if he loves him, Prospero responds: "Dearly."

Ariel acts as a contrast or foil to Caliban, a sullen, resentful slave who feels Prospero has taken advantage of him. Prospero has promised Ariel his freedom in exchange for helping him, and at the end of the play, he grants it to the spirit.

Ariel is Prospero's spirit servant. Ariel became Prospero's slave thanks to Sycorax, a witch (and Caliban's mother) who was on the island before Prospero. Sycorax trapped Ariel in a tree because he wouldn't follow her orders. When Prospero was exiled from Milan by his brother, he ended up on the island and struck a deal with Ariel: he would free Ariel from the tree on the condition that Ariel becomes his servant. Ariel agreed.
Later, Prospero gives Ariel his full freedom in exchange for Ariel's assistance in marrying off his daughter, invoking the tempest, and helping Prospero return to his proper place in society. In contrast with many of the The Tempest's human characters, Ariel is empathetic. His inherent virtuousness only makes the other characters' malice more apparent.
Unlike his fellow servant, Caliban, Ariel respects Prospero and fully believes that he'll one day make good on his promise to free him. Because he believes that he'll one day regain his independence, Ariel has a friendly relationship with Prospero, and is content to do what Prospero says. In fact, he believes in Prospero's integrity so much that Ariel views his master as his savior.