Most often, auras enter play after being cast. When they are cast, a target is chosen at that time. Then when the aura spell resolves, the aura enters the battlefield attached to the targeted permanent.

However, it is possible for an aura to enter the battlefield without being cast. In those instances the the aura will still become attached to a permanent in play. However as it is not being cast, it will not have a target chosen. What the aura enters play attached to will be decided by the player whose control that this aura would enter play.

For example, if an aura were to be exiled by Glimmerpoint Stag‘s triggered ability, at the end of the turn when this aura is returned to play it will become attached to a legal permanent of the choice of the controller of this aura. If you control both the Stag and this aura, you can use this combination to move an aura in play.