The friction contrafibulator was a button on the console of the Doctor's TARDIS. It appeared on both the War Doctor and the Eleventh Doctor's console first .
When Vincent van Gogh attempted to touch it, the Eleventh Doctor leapt across the TARDIS to stop him. (TV: Vincent and the Doctor)
Later, the Eleventh Doctor used the button to stabilise the TARDIS interior when the TARDIS was confused by the presence of the Eleventh, Tenth, and War Doctors. The Eleventh Doctor pressed the contrafibulator on the War Doctor's theme and the interior stabilised into the form of Eleventh Doctor's second control room. (TV: The Day of the Doctor)
Behind the scenes
Though the word is superficially technobabble, it's also a subtle connection to another Richard Curtis script: Blackadder the Third's Ink and Incapability. In that story Blackadder frustrates lexicographer Samuel Johnson by throwing out a few nonsense words — including contrafibularity — after Johnson has claimed that his dictionary contains "every single word" in the English language.
Breaking down this non-word to its real components, we find that it means contra (against) + fibula (the smaller of the two major bones of the leg) : "pulling one's leg".