A hologenerator, also known as a holographic generator or hologram generator, was a type of matrix-processing device used to create holographic imagery which was then displayed through holo-projectors.
After the Dominion took over the planet Yadera Prime, Rurigan fled his homeworld, taking with him a hologenerator, which he used to recreate everything he had lost on a new planet. (DS9: "Shadowplay")
Federation anthropological field teams used hologram generators for their "duck blinds", used for field studies of pre-warp civilizations. The reactor used to power such a device was capable of producing 4.2 gigawatts of energy. Such a device was used in 2366 to observe the Mintakans on Mintaka III. (TNG: "Who Watches The Watchers")
In 2369, Quark was negotiating to lease the space next door to his bar so that he could expand his holosuites while still using his existing holo-generators. (DS9: "If Wishes Were Horses")
After the crew of the USS Voyager transported over to the Caretaker's array in 2371, they discovered a simulation of a farm, which included the "Banjo Man" and a folk dance, Captain Kathryn Janeway had the away team, spread out and see if they could "find anything that might be a holographic generator." Harry Kim later found readings of "some kind of matrix-processing device," which suggested the presence of a holographic generator." (VOY: "Caretaker")
Later the following year, in preparation for battle with the Kazon, Voyager placed holo-projectors along the ship's hull to as to broadcast the illusion of additional ships present to aide in their defense. In doing so, however, they put a very high demand on the hologenerators before, putting into question whether an additional boost to the power input was necessary. (VOY: "Basics, Part I")