Canonicity

Canonicity, also called canon, was a concept that determined whether or not a certain source (such as a religious or fictional text) could count as a proper part of a greater whole; this concept was used by humans on Earth, whether they be practitioners of Christianity (AUDIO: The Council of Nicaea) or fans of the fictional adventures of Iris Wildthyme. (PROSE: From Wildthyme with Love)

However, many individuals within the Doctor's universe inexplicably questioned the canonicity of either their own adventures or those experienced by others, (AUDIO: Doctor Who and the Pirates, PROSE: Lady Peinforte, WC: The Story of the Diary of River Song) with the Time Lords even having a Tower of Canonicity. (PROSE: The Blue Angel)

Religious canon
In 325, the Council of Nicaea (to which the Fifth Doctor bore witness alongside companions Erimem and Peri) saw a gathering of the greatest scholars and leaders of 4th century Christianity to debate and solidify the reaches of biblical canon, showing the concept was applied by humans to religion. (AUDIO: The Council of Nicaea)

Fictional canon
Panda found out about the spin-offs from the Iris Wildthyme series from "super-fan" who "hardly knew what was canonical". (PROSE: From Wildthyme with Love)

By Time Lords and other time travellers
Canonicity was seemingly of interest to the Time Lords, as there existed a Tower of Canonicity in the Capitol, twin to the Tower of Likelihood. (PROSE: The Blue Angel)

The Sixth Doctor once expressed doubt on whether something to do with Hecate (about which he didn't elaborate) was "canonical". (AUDIO: Doctor Who and the Pirates, TV: A Girl's Best Friend)

The information contained on the TARDIS Wiki influenced Lady Peinforte's search for information on the Doctor, and she disbelieved that the Looms were canonical. (PROSE: Lady Peinforte)

The adventures experienced by River Song where she met her adoptive mother, her "sort-of" sisters, and various incarnations of the Master (including the War Master and Missy) were "probably" canonical. (WC: The Story of the Diary of River Song)

Behind the scenes

 * In the real world, canon is (as detailed on this page) a concept originally concerning religious texts, and later more widely applied to works of fiction, beginning with the tradition of Sherlock Holmes.
 * That the Time Lords and others such as the Sixth Doctor and River Song, whom are fictional characters, would thus consider canonicity a genuine property of their (fictional) universe, on par with "likelihood", should therefore be read as a borderline-fourth-wall-breaking, metafictional joke.
 * Whilst the song I Am the Very Model of a Gallifreyan Buccaneer contained numerous references to classic Doctor Who serials, the reference to Hecate was distinct in that it was derived from A Girl's Best Friend, the first and only installment of the spin-off K9 and Company.

Information from invalid sources
Ken Book interviewed Beep the Meep for Doctor Who Magazine, and after Ken asked if Beep had any plans to appear on television, he responded no, explaining it was a "backwards step" that'd be repeating what had already been done thirty years prior in The Star Beast, and ultimately, he didn't consider Doctor Who on TV to be canonical. He also added he was afraid they'd "do [him] in CGI". (NOTVALID: Who on Earth is... Beep the Meep)