It means they logged off or disconnected inside an instance or dungeon. The way the system works is it will register the character as online until they log back on and come back to their location on the real world.

Pro Tip: if you have more than one character on your account in the same world, you can log off inside a dungeon once it's done then log into your other character. Do a player search to find the first char and send a friend invite. It will work as it should show you as online in another world. Then log back into the fist character and can accept the friend request from yourself and thus be able to use moogle mail to transfer stuff between characters!