Aetheryte
Aetherytes are structures that are used to teleport to different locations within a city-state, and to different places within the world. Aetherytes vary in appearance depending on location.
The Aetheryte system within a city is called Aethernet.
As of Patch 4.57, the main Aetherytes in the starting city-states (Limsa Lominsa, Gridania, and Ul'dah) can be used to visit other World Servers.
A Residential District Aethernet is available in each city-state that contains a player housing area, allowing players to teleport to specified wards in the residential area.
Lore
These massive crystals can be found throughout Eorzea, allowing adventurers to travel great distances in an instant. When first attuning to an aetheryte, adventurers will learn the spells Return and Teleport, which are necessary to use these aetherial constructs. For the ever-wandering adventurer, attuning to as many aetherytes as possible will ensure swift transport to nearly any location.
Teleport destinations
Every city-state have one main, bigger, Aetheryte and many smaller Aetherytes called Aethernet Shards, each one marking its teleport destination, while other places in the world may have just the main Aetheryte in certain settlements. Most overworld zones contain more than one main Aetheryte. A list of teleport destinations can be found here.
Free Companies with housing can place an Aetheryte housing accessory on the outside garden: when the accessory is placed, its destination is automatically added to the Teleport list.
Attuning
When you attune to a main Aetheryte, its location will be added to your Teleport destination list. Attuning to the Aethernet Shard will add its location to the Aethernet destination list. When you attune to all existing Aethernet Shards of a city, your Aethernet list will get the city exit gates as new teleport destinations. Some aetherytes be visited but not attuned to unless the player has sufficiently progressed in the Main Scenario Quests.
System Messages
When attuned to all of the shards in each respective A Realm Reborn city-state
You now have Aethernet access to the Botanists' Guild.
You have attuned yourself to all the Aethernet shards in Gridania. The Blue Badger Gate, the Yellow Serpent Gate, and the airship landing are now accessible as Aethernet destinations.
You now have Aethernet access to the Blue Badger Gate (Central Shroud).
You now have Aethernet access to the Yellow Serpent Gate (North Shroud).
You now have Aethernet access to the airship landing.