Why does Shakespeare move the setting of the play Othello to Cyprus?
A key point about the action moving to Cyprus, I believe, involves the issue of Othello's military prowess and his loyalty to the Venetians.
Venice, and Europe as a whole at the time Othello takes place, felt vulnerable to attacks by the Ottoman (Turkish) Empire. The relatively recent fall of Constantinople, one of the last major outposts of the remnant of the eastern Roman (or Byzantine) Empire, was a shock to Europe. Othello, in spite of his non-European background, is a major part of the Venetian (and by extension European) effort to block the Ottoman advance and to protect the European continent.
In the second act it is revealed that a naval battle has taken place, and that the Venetians have defeated the Turkish forces. Othello's military ability, demonstrated here, is important to the action of the play, partly because it makes him an ideal husband to Desdemona for every reason despite the racist objections to him that have been raised. This demonstrates the wrongness of the racist views held by Brabantio and exploited by Iago.
In some sense the play can be seen as a metaphor of the conflict between European and non-European cultures. The setting in Cyprus, an island in the eastern Mediterranean which partakes of both cultures, is emblematic of that conflict. Othello himself is tragically caught in the middle, as a man of non-European descent giving his loyalty and love to the Venetians and to Desdemona.
The transition of setting from Venice to Cyprus puts Othello outside the immediate control of Venician authority and Desdemona beyond the disapprobation of prating Brabantio. It is the 'fleshing out' of sorts of their free will. An isolated military outpost symbolises both deliberate alienation from the norm and independance from control. Also, such liberty from primary influence serves as the vehicle for their respective natures to fully evolve and take hold.
But is such liberty too much? Here Othello's rashness and credulity- his double tragic flaw - is not held in check, for the 'veracity' of Iago and the sincerity of his friendship are never even put in question. As for Desdemona, her will melts before her idolation (and idealization) of her husband and she falls prey to Iago's perverse machination. She can no longer counter or even contest Othello's accusations once he is emported by rage. A subtle polarization of temperament has taken over. Whereas Desdemona weakens, Othello's hotheadedness now takes full rein and he loses control, he loses Desdemona, and he loses his life.
The island of Cyprus has important mythological significance as it has long been associated with Venus, the goddess of love. The action of The Tragedy of Othello moves to Cyprus when the Turks invade Venice, leading Othello and Desdemona to flee to the military encampment in Cyprus where they mistakenly believe their safety can be assured. Symbolically, this move to Cyprus is significant because the safety of Cyprus is a false one; Othello and Desdemona ironically lose their lives in a place where they were originally hoping to be safe. Another layer to the irony of this move relates to the fact that Iago's manipulation and his goals to ruin both Othello and Desdemona and to poison their love for each other are successful on an island that should be sacred to lovers thanks to its link to Venus.
Shakespere change the setting of the play from Venice to Cyprus so that all the characters are removed from the burning effects of the civil society and are released from Venice's influence and authority over them. It gives them independence from the "controlled" world they had.
It gives them liberty and gives them a portal to express their freedom and let their nature matarialized and evolve and take control over themselves