What dramatic function does the conversation between Montano and the two gentlemen serve? ( Othello, Act II, Scene i)
In addition to shakespeareguru's points, I might add that the discourse between Montano and the two gentlemen helps to establish Othello as a respected general. The men are obviously concerned for Othello's safety, as Othello has travelled through the same waters that shipwrecked the Turkish fleet. Further, Montano describes Othello as "a worthy governor," "Brave Othello," and says, "I have served him, and the man commands/ Like a full soldier."
In including these descriptions of Othello, Shakespeare helps readers understand how respected he is; this, along with the descriptions of his honorable role as a General in Act 1, makes his behavior in Act 3-5 even more shocking.
Also, Montano and the gentlemen discuss briefly note that Cassio, who has already arrived in Cyprus, is genuinely worried about Othello's safety:
But this same Cassio, though he speak of comfort
Touching the Turkish loss, yet he looks sadly
And prays the Moor be safe, for they were parted
With foul and violent tempest.
Here, Shakespeare establishes Cassio's loyalty to Othello by pointing out that while Cassio is happy that there won't be a war, he is upset because Othello's ship hasn't yet arrived. Again, as audiences realize that Cassio genuinely loves and respects Othello, they are later able to realize Othello's gross flaw in judgment (his misplaced trust in Iago, whom Othello didn't feel was worthy of the lieutenancy) and the ridiculousness of Othello's willingness to believe Iago's lies.
This is a really good question, rkturn! In theatre, especially on a stage like The Globe (where we assume Othello played), it is very important to keep the audience apprised of the location of each scene. This was especially true for The Globe, because it only had one "set," that remained the same for every scene in every play.
Act II of Othello requires that the audience travel from Venice to Cyprus, and Shakespeare's theatrical set-up at The Globe required this to happen without any change of sets. So the characters describe what they see in order to acclimate the audience to the new environment.
Act II, Scene i also serves to give the audience a transition between events. Montano and the Gentlemen are describing a very dramatic storm (which may have been underscored at The Globe with sound effects) that has destroyed the Turks' fleet off the ise of Cyprus. This information is being relayed to the audience in order to set up the landing and entrance of Othello, Iago, Desdemona, Cassio and the rest of their party at Cyprus.