A fluid link was a component of a TARDIS essential for providing power to the ship. Fluid links required mercury to function.
History
The earliest fluid links used validium, though rubidium would also function. Rassilon had dabbled at the prospect of subsisting the living metal for mercury, being convinced to do so when the Time Lord known as "The Other", in reality, the Eleventh Doctor, suggested it as a safer alternative. Trapped in Gallifrey's past, the Doctor had been seeking new fluid links to replace his evaporated ones only for Rassilon to bar him from them, eager to exploit his technical acumen. When the Doctor was testing a Type 1 TARDIS, he conspired to scavenge its fluid links as substitutes for his ship's only for the Type 1 to malfunction and trap him in the Void. (COMIC: The Lost Dimension)
The First Doctor falsely claimed that the TARDIS' fluid link—specifically, fluid link K7—had run out of mercury as a ruse to explore the Dalek City. The link was later confiscated by the Daleks and accidentally left behind in the city, forcing the time travellers to help the Thals fight the Daleks to recover it. (TV: The Daleks) While the TARDIS was being brought to the Animus by the Zarbi, Vicki accidentally re-aligned the fluid link, which restored power to the ship. (TV: The Web Planet)
A malfunction caused the fluid links to explode, filling the TARDIS with mercury fumes and forcing the Second Doctor and Jamie McCrimmon to evacuate the TARDIS. (TV: The Wheel in Space) The fluid links overheated again when the TARDIS was caught in a volcanic eruption on Dulkis. The Doctor was forced to take the TARDIS out of reality itself. (TV: The Mind Robber) When trying to navigate the rings of Saturn, the Doctor was afraid the fluid links would become damaged. (PROSE: The Wheel of Ice)
The Fourth Doctor and Sarah Jane Smith rescued a ship from a pirate fleet of Grakinese Corsairs by exchanging with them some mercury from a fluid link. They got some more mercury in 1931 Chicago, unknowingly defeating the Master's plans in doing so. (PROSE: The Duke of Dominoes)
When an alien creature broke into the TARDIS, it began leeching the ship of power, affecting the function of the fluid links. (PROSE: Cat's Cradle: Time's Crucible)
The fluid links ran out of mercury again, forcing the Seventh Doctor to steal some from the Wierdarbi with the aid of Catherine Broome. (PROSE: Companion Piece)
Ace, as part of mourning the loss of Hex, removed the fluid links to stop the Doctor gallivanting across the universe. (AUDIO: Afterlife)
The fluid links ran out of mercury again, forcing the Eighth Doctor to materialise on a podule orbiting Jupiter in search of some. (PROSE: To the Slaughter)
The Eighth Doctor visited Rontan 9 during the Last Great Time War in search of mercury to repair his TARDIS' fluid links. (PROSE: Natural Regression)
The Tenth Doctor visited Calibris on 31 May 2008 in order to obtain a new fluid link. (AUDIO: Time Reaver)
Nardole, in his attempts to keep the Twelfth Doctor at the university where they had been guarding the Vault, removed the fluid link K57 from the TARDIS during one of the Doctor's lectures. Although the Doctor told Nardole that the TARDIS would not operate without it, this was a lie, and the TARDIS was still able to take off. (TV: Oxygen)
Behind the scenes
The fluid link is a defining plot point of the theatrical film Dr. Who and the Daleks, adapted from TV: The Daleks. This wiki does not consider the Peter Cushing Dalek films to be a valid source for writing articles.
As recounted by Susan Foreman in NOTVALID: Whatever Happened to Susan Foreman?, the Daleks, having been defeated on Skaro by the Thals led by Ian Chesterton, used their own TARDIS to travel into the past with the intent to wreck revenge on Ian's people or, better still, prevent Ian himself from being born. However, they were unable to go any further back than 2164 due to a leak in their fluid link, resulting in the 22nd century Dalek invasion.
The BBC concept art for River Song's sonic screwdriver depict a small tubular attachment listed as a "fluid link" along one side of the device, leading up to a section with a blue button, referred to as a TARDIS recall button.