Holograms were projections of light by a laser beam (TV: The Talons of Weng-Chiang) which cast three-dimensional images used for information storage and communication. Some holograms were also capable of developing sentience or being used to recreate life.
Holograms were usually projected from a device, meaning that they were generally stationary. Some were mobile, however, and appeared not to be connected to a projector, at least not visibly.
A type of holograms, hologlyphs, could materialise and dematerialise at will or when summoned, could be programmed not to know they weren't real, and could have a solid feel to them as if they were real beings. A hologlyph of a recently deceased person could even be created to acquire as to the last few moments of their life. They were also able to interact with machinery, as Book was able to connect with the lexicon. (AUDIO: ...ish)
Xanxia was able to create a permanent cellular regeneration projection of herself, always nearly complete but forever connected to the real Xanxia whose near-dead body was preserved between two time dams. The Doctor could not switch her off, and was even slapped by her. She could also physically interact with her surroundings and her personal devices, which might have been projected as well, were also physical. (TV: The Pirate Planet)
Instances of hologram use
In 1938, with little time left, the Eleventh Doctor used the TARDIS' voice interface, which variously took on the images of Rose Tyler, Martha Jones, Donna Noble and Amelia Pond. (TV: Let's Kill Hitler)
In 2007, when Sally Sparrow inserted a DVD with the Tenth Doctor's message to her into the TARDIS console, it opened a projection of the Doctor, who announced the TARDIS was returning to his timestream. (TV: Blink)
In 2008, the Eleventh Doctor called the Atraxi back to check if Earth violated their laws, and if it was defended, which the Atraxi confirmed with holograms. The holograms showed Pete's World Cybermen, Daleks flying out of the Genesis Ark, Dalek Sec, a Sea Devil, a Reaper, a Sontaran, the Empress of the Racnoss, Vashta Nerada operating a spacesuit, Hath, Ood and a Sycorax for those who had attacked Earth in the past. For its protector, it showed the First, Second, Third, Fourth, Fifth, Sixth, Seventh, Eighth, Ninth, and Tenth incarnations of the Doctor. (TV: The Eleventh Hour)
Captain John projected an image to Torchwood of a canister containing what he thought was part of a key to find an Arcadian diamond, but were actually parts to a bomb that attached to the DNA of whoever killed the woman that owned this canister. When Captain John, the woman's murderer, assembled these pieces, it projected a hologram recording of this woman to tell him this. (TV: Kiss Kiss, Bang Bang)
In 2011, the Skullions under order of Harrison made and controlled a hologram of Joseph Serf during the release of the SerfBoard. This hologram had hypnotic powers that willed people to buy the SerfBoard. Luke and Sky Smith later took control, telling the journalists at the release that the SerfBoard was junk. (TV: The Man Who Never Was)
A hologram of Mel Bush was created by the Rani to trick the Doctor into giving her back a component of her Time Manipulator. The hologram could move like her and disappeared when the Doctor tried to embrace her. (TV: Time and the Rani)