In Act 3 Scene 1, What is the purpose of the conversation between Cassio, Iago and Emilia from lines 30 onward?

This is setting up Iago's plan to further cast suspicion on Cassio by setting up a meeting between Cassio and Desdemona.Cassio will entreat Desdemona to plead his case to Othello. This of course, in the end serves to ignite the moor against his wife and fulfill this tragedy.

By reading these lines we see where Emilia's sympathies lie, and that she is a willing go between in the entire situation concerning Cassio's reinstatement (and many other intrigues within the plot) Through her, information makes its way to those its intended for, and she is greatly trusted with the information she carries. She's also requested to "watch" the things going on around her (particularly in regards to Desdemona), while Othello is advised to watch Desdemona's reactions as well. It's a vicious circle, that's for sure!