During the game Yuna goes to 6 different temples. In each temple you must go through what is called the Cloister of Trials, here you go through and solve each trial. To pass each trial, numerous spheres must be rearranged into various slots to open a pathway through. There are certain spheres and glypths that do certain things.
After you make your way through and get to the end of each Cloister of Trials you recieve a new aeon. There is a treasure chest in each temple if you collect them all you can use the airship to fly somewhere and get a secret aeon!