When analyzing a passage, it helps to first look for different literary devices and then figure out what the author could be conveying with these devices. Common devices to analyze for can be mood, tone, theme, characterization, figurative language, and diction. Specifically, some interesting elements in this scene are the moods that Feste creates as well as an important theme that he illustrates.
One thing we see about the mood of the scene is that it's very ironical. We can especially hear the ironical mood in Feste's lines. For example, he states that he is neither tall enough to play a good curate nor lean enough to be considered a biblical scholar. However, regardless, he is still donning the curate's gown and beard. Beyond being ironical, the mood progresses to being rather dark as we begin to hear just how much Malvolio is being tormented in his dark enclosure and hear him begging for help. This dark mood contrasts with the lighter, gayer mood of the play and also directly parallels the final scene, which ends on a sadder not than would be expected. The dark mood helps portray the harshness of reality, which Feste later sings about in his final song.
Feste also portrays the theme of appearances vs. reality. He illustrates the theme of appearances vs. reality by of course pretending to be the curate, but he also makes a very important claim in this scene. Feste asserts that reality is unimportant because illusion creates the reality, as we see in his lines:
'That that is, is.' So I, being master parson, am Master Parson; for, what is 'that' but 'that'? and 'is' but 'is'? (13-15)
Hence, even though Malvolio may not really be mad, if the other characters, such as Feste, create the illusion that he is mad, then madness becomes the reality.