Thought Elevator is a term used by those affiliated with Code-R 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 presumably Area 18. There are presumably 8 or 9 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.
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.
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 "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.