A Time Vector Generator was a component of a TARDIS that made it dimensionally transcendental. Removal of the Time Vector Generator would collapse its interior into an alternate dimension, leaving only the exo-shell and making it the same size on the inside as the outside. As the Second Doctor succinctly put it, removal of the TVG turned the TARDIS interior "into an ordinary telephone box again". (TV: The Wheel in Space)
It resembled a long ebony wand and was a powerful energy source.
The Doctor removed the TVG when the fluid links exploded, filling the TARDIS with mercury fumes. The TVG was later used to boost Space Station W3's x-ray laser to defeat the Cybermen. (TV: The Wheel in Space)
Also, the Third Doctor stated that TVG could send someone to the future. The Third Doctor activated the TVG while the console was disconnected due to repairs in the TARDIS and accidentally sent himself and Liz Shaw to the future only for 15 seconds. (TV: The Ambassadors of Death)
When the Seventh Doctor confronted a clone of his predecessor created by the Forge, the clone initially claimed to be the true Sixth Doctor, who had removed the TVG from the TARDIS to prevent the Forge acquiring its technology. However, the Seventh Doctor realised that this was a lie as the TARDIS exterior's invulnerability could still have been useful to the Forge even without the TVG. (AUDIO: Project: Lazarus)