The term ‘moor’ refers to those born in Mauritania, or present day North Africa. It is likely that the term is used so frequently in the opening scene to emphasise to the audience the uniqueness of Othello as a member of Venetian society. The term helps to quantify Othello as different: an outsider with an exotic and mysterious origin. The audience will hopefully be as compelled to learn his tale as the innocent and compassionate Desdemona--and indeed the Senate.
I think this tale would win my daughter too.
It is said that Othello’s origins were also revealed as it was believed at this time that one of the qualities of a Moor was jealousy. It is possible that the term is repeated to establish Othello’s fatal flaw in the minds of the audience, even before, of course, he is even introduced as a character in his own right.