Aura is an enchantment subtype that has the text "Enchant [type or player; restriction]". Formerly, Auras were known as "local enchantments" or "enchant [type]" cards. The name was introduced in Ninth Edition. 
From the Comprehensive Rules
(Battle for Zendikar
(September 26, 2015
303.4. Some enchantments have the subtype “Aura.” An Aura enters the battlefield attached to an object or player. What an Aura can be attached to is defined by its enchant keyword ability (see rule 702.5, “Enchant”). Other effects can limit what a permanent can be enchanted by.
- 303.4a An Aura spell requires a target, which is defined by its enchant ability.
- 303.4b The object or player an Aura is attached to is called enchanted. The Aura is attached to, or “enchants,” that object or player.
- 303.4c If an Aura is enchanting an illegal object or player as defined by its enchant ability and other applicable effects, the object it was attached to no longer exists, or the player it was attached to has left the game, the Aura is put into its owner’s graveyard. (This is a state-based action. See rule 704.)
- 303.4d An Aura can’t enchant itself. If this occurs somehow, the Aura is put into its owner’s graveyard. An Aura that’s also a creature can’t enchant anything. If this occurs somehow, the Aura becomes unattached, then is put into its owner’s graveyard. (These are state-based actions. See rule 704.) An Aura can’t enchant more than one object or player. If a spell or ability would cause an Aura to become attached to more than one object or player, the Aura’s controller chooses which object or player it becomes attached to.
- 303.4e An Aura’s controller is separate from the enchanted object’s controller or the enchanted player; the two need not be the same. If an Aura enchants an object, changing control of the object doesn’t change control of the Aura, and vice versa. Only the Aura’s controller can activate its abilities. However, if the Aura grants an ability to the enchanted object (with “gains” or “has”), the enchanted object’s controller is the only one who can activate that ability.
- 303.4f If an Aura is entering the battlefield under a player’s control by any means other than by resolving as an Aura spell, and the effect putting it onto the battlefield doesn’t specify the object or player the Aura will enchant, that player chooses what it will enchant as the Aura enters the battlefield. The player must choose a legal object or player according to the Aura’s enchant ability and any other applicable effects.
- 303.4g If an Aura is entering the battlefield and there is no legal object or player for it to enchant, the Aura remains in its current zone, unless that zone is the stack. In that case, the Aura is put into its owner’s graveyard instead of entering the battlefield.
- 303.4h If an effect attempts to put a permanent that isn’t an Aura, Equipment, or Fortification onto the battlefield attached to an object or player, it enters the battlefield unattached.
- 303.4i If an effect attempts to put an Aura onto the battlefield enchanting an object or player it can’t legally enchant, the Aura remains in its current zone.
- 303.4j If an effect attempts to attach an Aura on the battlefield to an object or player it can’t legally enchant, the Aura doesn’t move.
- 303.4k An ability of a permanent that refers to the “enchanted [object or player]” refers to whatever object or player that permanent is attached to, even if the permanent with the ability isn’t an Aura.
- ↑ Mark Gottlieb. (July 29, 2005.) "Aura Hygiene", Daily MTG, magicthegathering.com, Wizards of the Coast.
- ↑ Mark Rosewater. (June 07, 2010.) "Disadvantaged", Daily MTG, magicthegathering.com, Wizards of the Coast.
- ↑ Tom LaPille. (June 11, 2010.) "Potpaurai", Daily MTG, magicthegathering.com, Wizards of the Coast.
- ↑ Doug Beyer. (June 09, 2010.) "Auratouched Magery", Daily MTG, magicthegathering.com, Wizards of the Coast.