Thought Elevator is a term used by those affiliated with Code R Research Team to designate structures linked with the Geass ability. Bartley Asprius speculates that some of the Emperor's recent invasions were done to gain control of the devices.
In appearance they are shown as an enormous vertical gateway from which bright light streams. Only two have been shown so far, on Kamine Island and another in the Geass Directorate's city and Area 18. There are eight of them around the world as shown in episode 17 of Season 2. It is hinted that they were constructed by some long-forgotten ancient civilization. The three international superpowers each have at least one, excluding the one at the South Pole. The Europia United formerly had the most Thought Elevators with three falling within their territory, including one apparently existing underneath the E.U. occupied Britannian city of London, but after the Second Season the Holy Empire of Britannia had the most Thought Elevators numbering about five after capturing Africa, Russia and Area 18. The Chinese Federation has at least two, with one located in the Militarized Zone of India and the other in Northwestern China located inside the Geass Order based. There was also one apparently located beneath Pendragon Imperial Palace which allowed Charles to enter the Sword of Akasha any time he wished.
While the Thought Elevators' true functionality is not clear, they are known to work through a person's memories or thoughts. Lelouch determines this after experiencing one firsthand, basing his hypothesis upon his earlier escape from C.C.'s memory zone by the thought of wanting to help her. When Lelouch questions C.C. about having some connection to the thought elevator on Kamine Island she responds "not this one," indicating that she has a connection to another thought elevator.
Another function of the Thought Elevators is to facilitate the Ragnarok Connection and the "activation" of the Sword of Akasha. Charles zi Britannia was able to travel to the Sword of Akasha via one of the Thought Elevators, and the Sword's ultimate function, killing the Gods, was facilitated by the thoughts and feelings of all humanity -- the collective unconscious, or C's World -- being connected and focused on the Sword of Akasha via the Thought Elevators.