There are a lot of birds on the island, but not the pretty tropical kind you might expect. The island is swarming with grandfather birds (which trousermen call trouserbirds. Make of that what you will!). And these birds are not charming little songbirds. They are "very clumsy and didn't so much land as crash slowly (2.133), and often fill the air with the musical "sound of throwing up" (2.133). Glad we don't have to wake up to that.
Oh, Mau also believes that "the birds were spies for the Grandfathers and would swoop on you and peck your eyes out if you came too close" (2.58). Ugh, these things just keep getting better.
Not only does Mau have the grandfather birds to contend with, but then Daphne comes along with that awful parrot. It pretty much just flies around and swears a lot: "Some of the words it came out with a respectable young lady should not know the meaning of" (3.7).
So what's the deal with all these birds? Perhaps the grandfather birds represent tradition (creepy, crusty, moldy old tradition) and the parrot represents European conquest, and all the crass disrespect that comes with it. At least the parrot didn't come wrapped in a smallpox-infested blanket. Yikes.
Or, hey, maybe they're just the comic relief. A book about a shipwreck and a title wave needs something to lighten the mood a bit, and a parrot asking you to show it your underwear is just the trick.