The significance of thise scene in the play seems best summed up in Fabian´s comment:
If this were played upon a stage now, I could condemn it as an improbable fiction.
What happens in this scene are a series of further plot complications that further confuse identities, relationships and make more problems for the central characters as we see the key themes of deception and mistaken identity further advanced.
First of all we see the fruits of Malvolio´s successful gulling by Maria and her cronies. He protests his love for Olivia, coming forward in his yellow-gartered stockings. Olivia is of course amazed, and her response reflects the theme of love as madness:
Why, this is very midsummer madness!
Love makes us do stupid things, and at various points in the play love is described as a disease or a sickness that we suffer from. Also, we see in Malvolio´s responses to Olivia´s shock that when we suffer from the "disease" of love we twist everything to make it fit "our" facts. Malvolio sees everything as further proof of how correct his assumptions are, just as we are prone to when we are infatuated with someone.
Note too, how Malvolio´s behaviour enables Maria and Sir Toby and Feste to continue to have their fun with Malvolio and get their revenge. As Olivia considers Malvolio is mad, they can do what they want to him, which they do.
The duel between Viola and Caesario adds another comic element to the play. Note how Sir Toby scares each of them with the supposed prowess of the other. Then Caesario is mistaken for his brother by Antonio, this mistaken identity becomes further complicated and rather tragic when Antonio is arrested and needs the money he has given to Sebastian. Of course, Caesario is incredibly confused by this. Antonio´s continued protestations that he knows Caesario convince his captors that he is insane. Note how mistaken identities and love leads to accusations of insanity - this scene then represents the world of Twelfth Night swinging out of control. Anarchy seems to rule this world, and the audience begins to wonder how all of these crossed lines of communication can be rectified.