Tri-D is a type of television which was used throughout the Universe. A tri-D robot camera was filming the events on Damogran when Zaphod Beeblebrox arrived to reveal the Heart of Gold to the public, and subsequently steal it.
One way in which tri-D was recorded was using a small robot camera, which hovered around and filmed through its "eyes." At one point in the first novel, the robot tri-D camera honed in for a close up of the more popular of Zaphod's two heads. It is unknown if these robot cameras had artificial intelligence or not, however, unlike many other robots in the series, it does not speak or attempt to communicate.
The use of tri-D seemed to be popular; three million people were said to be watching the events on Damogran through the eyes of the robot. Zaphod's antics as President of the Galaxy were said to always make "amazingly popular" tri-D.
The name tri-D is a reference to the use of 3-D or three-dimensional filming, which makes viewers feel as though they are witnessing the events they are watching first hand by having the images on the screen appear in three dimensions instead of two. Tri-D possibly has a similar effect, however, it could just as likely be very similar to 2-D filming.
In Fit the Fourth a similar type of television called Five-D is mentioned, with the mice Frankie and Benjy saying that they have secured a contract to do a "Five-D T.V. chat show and lecture circuit." It is likely that this is a five-dimensional type of television viewing.