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The Relative Dimensional Stabiliser (simply called RDS or, more often, dimensional stabiliser) was a component of a TARDIS control system, which allowed to cross the dimensional barrier (TV: The Invisible Enemy) or, in other words, which regulated the outer plasmic shell of the ship in relation to its exterior.
Some of its functions and/or components include a chronostat and "synaptic adesion". (TV: The Armageddon Factor)
TARDIS
The relative dimensional stabiliser field prevented Andred from firing his staser in the Doctor's TARDIS. (TV: The Invasion of Time)
The Fifth Doctor asked if there was a problem with the dimensional stabiliser, causing turbulence. (TV: Time-Flight)
On one occasion, space pressure reduced both the interior and the exterior of the Doctor's TARDIS to minute size without affecting the passengers adversely. (TV: Planet of Giants)
On Moldox, the War Doctor and Cinder jumped into his crashed TARDIS, laying on its side, and found themselves the right way up. He explained to her that the relative dimensional stabilisers prevented them to "fall", since the inside could be orientated differently to the outside. (PROSE: Engines of War)
Other uses
The item could be used to change the dimensions of living beings or other external targets. In 5000, Professor Marius used the relative dimensional stabiliser of the Doctor's TARDIS to shrink down clones of the Fourth Doctor, Leela and Lowe, and enlarge the Nucleus of the Swarm, bringing it into the macrocosm world. (TV: The Invisible Enemy) By using the dimensional stabiliser of the Drax's TARDIS, the Fourth Doctor and his fellow Time Lord reduced their own size in order to catch the Shadow. (TV: The Armageddon Factor)
The Sixth Doctor expanded the dimensional stabilisation field of Straxus' TARDIS to an entire pocket dimension he was trapped in by a machination of the Master; this let four other incarnations of the Doctor (the Fourth, the Fifth, the Seventh and the Eighth) to fully materialise with their own TARDISes in the dimension itself. This use of the RDS implied the destruction of the Straxus' TARDIS. (AUDIO: The Light at the End)
Behind the scenes
The video game Attack of the Graske referred to the dimensional stabliser in a gameplay mechanic as a yellow lever that helped the player at home fly the TARDIS to 19th century Earth. This same lever was operated by Sarah Jane Smith in Journey's End to assist in returning the Earth from the Medusa Cascade.
As Attack of the Graske involves multiple choices of endings, this wiki does not consider it a valid DWU source.
In Russell T Davies' book The Writer's Tale, the full original draft of Journey's End has the Tenth Doctor stating that it takes "thousands of years" to grow a TARDIS. However, Donna uses her newfound Time Lord knowledge enhanced by human intuition to overcome this problem by suggesting: "...if you shatterfry the plasmic shell and modify the dimensional stabiliser to a foldback harmonic of 36.3, you accelerate growth by the power of 59!", which would presumably enable a TARDIS to grow within a human lifetime. The scene is included as a bonus feature with the series 4 DVD box set released in November 2008.