What is the purple & black building that sits atop the rock bluff to the right of the airport?

That is the Aviary. You will receive that landmark after you complete the other four (lighthouse, chapel, pirate ship, and mountain chateau), around the 2 year mark of your game. Once you reach level 6 of the Aviary, you will be able to select from 4 bird breeds and hatch and release them to fly on your island. It is a way to continue adding Flower value to your island daily.

It is the Aviary. When a person has upgraded all the other landmarks you get to build it. So in order you upgrade the Lighthouse, the Wedding Chapel, the Pirate Ship, and the Mountain Chateau.Then when all those are fully upgraded the Aviary is built.