See that ornate circle in the middle next to Felix? That's a Teleport circle. If you use teleport there, which you get in Mars Lighthouse, then it will transport you to the Anemos Inner Sanctum. If you have all the djinn then it will give you a summon, Charon, and then you can continue through a series of puzzles, which I have never bothered to do becuause it's optional. However, if you get to the end, then there's a boss, Dullahan, and he is the hardest boss in the game, even harder than the Doom Dragon. If you defeat him, then you get Iris, a summon which heals and revives all your people, and deals extremely fierce damage against the enemy. Very useful for taking on the Doom Dragon.
On a side note, you see that piece of corn aside from the others on the table? If you go up to it and press then you will aquire it. Corn heals one of your party 100hp. BACK!