The Clown has two scenes of importance. The first, in Act III.i, with the musicians, is more for comic relief, as he makes references to those people who are like "wind instruments" (full of hot air). This is a light-hearted pun poking fun at the male characters in the play, namely Iago, who is full of hot air. He lies to everyone he meets ("I am not what I am"). Also, as the Enotes editor says:
When they [the Musicians] play, a clown comes out and comments on the quality of their music by asking, “Why, masters, have your instruments been at Naples, that they speak i’ th’ nose thus?” An Elizabethan audience would be quick to pick up on the bawdy pun on the word instrumentsand the suggestion of the poor health conditions of the city of Naples.
The second Clown scene, Act III.iv, is used more for foreshadowing. Desdemona asks the Clown, "Do you know, sirrah, where Lieutenant Cassio lies?" She means the past tense of "lay," but the clown makes a pun on the word, meaning an "untruth." The Clown says, "He’s a soldier, and for one to say a soldier lies, ’tis stabbing." In other words, "If I accuse a soldier of lying, I'll get stabbed." This is ironic, as Othello will accuse Desdemona of lying, will accuse Cassio of drunkenness, will accuse Emilia of lying, but he will not accuse Iago, a soldier, of lying. Instead, he calls him "Honest Iago" repeatedly. Again, the Enotes editor:
The clown, who is Othello’s servant, in this scene provides some comic relief to offset the intensity of the previous scene. When Desdemona asks him if he knows “where Lieutenant Cassio lies” he responds by saying “I dare not say he lies anywhere. … He’s a soldier; and for one to say a soldier lies is stabbing.” The pun on the word lie is made when Desdemona asks for Cassio’s whereabouts, but the clown responds as if she had called him a liar. The dramatic irony with this pun is clear because Iago’s whole scheme is based on the lie of Desdemona’s infidelity.