In the first two acts Othello, Iago has been weaving a web of treachery and deceit, planting seeds that will spark the fire of jealousy later. Enough already!
Shakespeare wisely buffers Iago's plotting and the beginning of Othello's rage with this brief comic scene. The domestic tragedy would be too heavy without it. This respite from the seriousness of the play gives the audience pause, just for a moment, before the raging fall of Othello occurs in Acts IV and V.
The scene appeals to the lower classes of Elizabethan society, to the groundlings (the uneducated), who need a laugh between the ponderous monologues and soliloquies. It's all about pacing and appeal to audience. In this, his most focused tragedy, Shakespeare takes his foot off the gas for a little bawdy humor pitstop.
So says Enotes:
This scene provides some comic relief from the drama that has transpired in the previous act. Cassio’s request for the musicians to serenade Othello and Desdemona reflects the Elizabethan custom of awakening people of high rank with serenades on special occasions. When they 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 clown then sarcastically says that Othello likes the music so much, he will pay the musicians to stop.