How is the nature of civilization relevant to Shakespeare's Othello?

One of the themes of the play is the nature of what people consider to be civilized. Within the world of the play, Venice represent the "civilized" European world and Othello, as a Moor, is a "barbarian" or outsider.
The first issue you should address in your essay is the historicity of this viewpoint. The play is set in Venice in the sixteenth century. At this period, the Ottoman Empire had conquered Constantinople and was vast and powerful. The Moors (followers of Islam of Arabic or North African descent) were also powerful and possessed a venerable and sophisticated civilization which, unlike the Latin West, had not collapsed into a "Dark Ages" but maintained continuity of knowledge; much of the European Renaissance, in fact, had been due to recovery of ancient learning via contact with the Moors in Spain. Thus, although the play presents Venice as civilized and the Moor as originating outside "civilization," those labels are not historically accurate.
Next, we can also problematize the concept of civilization by looking at the qualities of the characters in the play. Many of the members of Venetian society, despite a veneer of polite manners, are the true moral barbarians, duplicitous, longing for material wealth and position, and morally corrupt. Iago, a noble Venetian, is much less honorable than the barbaric Othello. 
Finally, we might look at the military background of the play and argue that both Venice and the Ottoman Empire are in Cyprus for identical reasons of promoting mercantile and territorial advantage. Both great civilizations are shown here as equally rapacious and, in a sense, "uncivilized."