Teleporting plates are normally found on the ground but at the Flying Fortress you are the person to place it as part of a quest. The teleporting plates are indicators that shows you where you will get teleported to when you choose your destination on the map, found in the menu (press ESC).
To teleport to a teleportation plate you must first have walked over it to activate it. The teleportation plate in Evergrind City and the teleportation plate for the Flying Fortress gets activated as soon as you turn into a collector/place the teleportation plate down (probably to ensure that players can leave and return to the Flying Fortress) but all the other plates require activation.
After a teleportation plate has been activated it gets added to your map, indicated by a yellow ring around a green dot.