Why is the war between the Turks and Venice important for the play Othello?
Shakespeare's depiction of the threat of the invasion of a Turkish fleet upon the island of Cyprus, a strategic holding of the Venetians since 1423, is important to the plot of Othello because it is the literary vehicle which draws Othello and Desdemona away from the sophisticated and civilized setting of Venice. This move thus allows the miscreant Iago a facile setting for his treacherous plot against Othello apart from Desdemona's father and other members of the court. Figuratively, too, the setting of Cyprus versus that of Venice mirrors the conflict between the noble Othello and the malevolent Iago.
Though I do hate him as I do hell-pains.
Yet, for necessity of present life,
I must show out a flag and sign of love,
Which is indeed but sign. (1.1.12)
In this quote, Iago expresses his hatred of Othello in terms of warfare--"show out a flag" as on a ship--a metaphor that underscores the conflict of man vs. man and the theme of deep suspicions as reflective of larger ones such as the Venetians vs. the Ottomans and the tremendous suspicions that Venetian Christians had of the Islamic empire.
Not unsurprising, however, is the fact that the war between the Turks and the Venetians is historically incorrect in Othello as Shakespeare dismisses the threat of the Turks by having a fortuitous storm destroy only the Turkish ships while the Venetians arrive safely on shore so that the plot of Iago against Othello can continue without interference.
The war between the Turks and the Venetians (and circumstances surrounding it) can also be seen as metaphors for certain themes in Othello.
1. The theme of deception: While Iago deceives Othello, the Turkish army also tries to trick the Venetians. In Act 3 Scene 1, the Duke, Senators, and Officers realize that though reports say the Turkish ships are headed to Rhodes, it is much more likely that the ships are headed to Cyprus. This contrasts to the gullibility of Othello, who is unable to discover Iago's deception.
2. The theme of passion blinding reason: War is often characterized by gruesome deaths and wanton killing. As such, (as mwestwood mentioned) it is a fitting vehicle to bring Othello and the others to the island of Cyprus. This is because Venice can be seen as a place of stable ground and solid reason, whereas Cyprus is an island awash in a sea of emotions. Swept here by the war, Othello succumbs to the passions of jealousy, Cassio falls from drunkenness, and even Desdemona, blinded by love, fails to see her precarious situation.
3. This may be a stretch, but no harm mentioning. Wars often result in many useless killings. Iago and his machinations also result in many useless deaths. As such, the war can be seen as a parallel to the tragic outcome of this play.