A dematerialisation circuit was an essential part of a Type 40 TARDIS which enabled it to dematerialise from normal space into the Vortex and rematerialise later back into it. (DW: Terror of the Autons) It did a slow appear/disappear into universes, and a fast appear/disappear in the Time Vortex. (This is shown on the 2005-2010 opening title animation, where it appears just before flying on to the screen and disappears just after the name of the episode is shown.) This was because of the absence of gravity and other forces in the Time Vortex because the Time Vortex does not exist in a universe - it exists outside all of them.
During his exile on Earth, the Time Lords removed the "dematerialisation codes" from the Doctor's mind and made the dematerialisation circuit of his TARDIS inactive. He therefore coveted the working dematerialisation circuit of the Master's TARDIS (DW: Terror of the Autons, The Mind of Evil, EDA: The Eight Doctors). Once the Time Lords had rescinded his exile after his defeat of the renegade Time Lord Omega, the Time Lords restored this knowledge to the Doctor's memory. (DW: The Three Doctors)
Dalek time travel devices contained mini-dematerialisation circuits. (DW: Day of the Daleks)