Aurae are wind nymphs that are commonly mistaken for ghosts. Their bodies are composed of fog. They usually appear as women, although it is unknown if they have other forms that they can take (it is possible, as storm spirits can).
Jason Grace, Piper McLean, Leo Valdez, and Gleeson Hedge meet an aura named Mellie, who works for Aeolus, but is fired after saving the four of them. Mellie then gets a new job and starts working for Tristan McLean.
Auras have some power over the air, as Mellie was able to save Jason, Piper, Leo, Coach Hedge and herself from what would have been a deadly fall, albeit with help from Jason. It is unknown how an aura's 'wind strength' compares to a demigod's power, but it can be assumed they are weaker, as the river naiad (water equivalent of an aura) from the Triple G Ranch appears scared that Percy Jackson might overpower her and force her river to clean the stables, as this has happened before. It can therefore be assumed that auras tend to be weaker than demigods when it comes to sheer power.