Aeons are similar to the GFs from previous FFs. They are spritual beings called upon to protect Yuna.
Valefor [1] [2]
Valefor is an aerial aeon. He has very high accuracy and is quick. He is acquired in the Besaid Temple.
Ifrit[1]
Ifrit is the 'fire' aeon. He has a very high strength, but low defense and magic defense. Ifrit can be found in Kilika Temple.
Ixion
Ixion is found in the Djose Temple. His specialty is protecting the party. He has high defense and magic defense.
Shiva
Shiva has been in the past FFs. She is an agile attacker and is the 'ice' aeon. She resides in the Macalania Temple.
Bahamut
Bahamut should also be familiar since he was in the other FFs as well. His specialty is magic, defense, and strength, and can be found in the Palace of St. Bevelle.
Yojimbo
In the Cavern of the Stolen Fayth is where you can find Yojimbo. Remember that he is a secret aeon (don't tell anyone!!) To get him on your side, you must fight him. Every time you summon him, you must pay him so that he'll do something.
Anima
Defeat Geosgaeno in the Baaj Temple to get this aeon. Go to the underwater temple where the statues inside Anima's shrine are. Then you see Anima...
The Magus Sisters
Back from Final Fantasy IV, the Magus Sisters are in the Remiem Temple. You have to defeat all of the enemies in the Mt. Gagazet area, then go back to the monster arena and get the Blossom Crown. After that, go back to the Remiem Temple. Defeat Belgemine's aeons and receive the Flower Scepter. Then open the door with the keys and you get the Magus Sisters.