[very common; historically, ‘according to religious law’] The usual or standard state or manner of something. This word has a somewhat more technical meaning in mathematics. Two formulas such as 9 + x and x + 9 are said to be equivalent because they mean the same thing, but the second one is in canonical form because it is written in the usual way, with the highest power of x first. Usually there are fixed rules you can use to decide whether something is in canonical form. The jargon meaning, a relaxation of the technical meaning, acquired its present loading in computer-science culture largely through its prominence in Alonzo Church's work in computation theory and mathematical logic (see Knights of the Lambda Calculus). Compare vanilla.
Non-technical academics do not use the adjective ‘canonical’ in any of the senses defined above with any regularity; they do however use the nouns canon and canonicity (not **canonicalness or **canonicality). The canon of a given author is the complete body of authentic works by that author (this usage is familiar to Sherlock Holmes fans as well as to literary scholars). ‘The canon’ is the body of works in a given field (e.g., works of literature, or of art, or of music) deemed worthwhile for students to study and for scholars to investigate.
The word ‘canon’ has an interesting history. It derives ultimately from the Greek κανον (akin to the English ‘cane’) referring to a reed. Reeds were used for measurement, and in Latin and later Greek the word ‘canon’ meant a rule or a standard. The establishment of a canon of scriptures within Christianity was meant to define a standard or a rule for the religion. The above non-techspeak academic usages stem from this instance of a defined and accepted body of work. Alongside this usage was the promulgation of ‘canons’ (‘rules’) for the government of the Catholic Church. The techspeak usages (“according to religious law”) derive from this use of the Latin ‘canon’.
Hackers invest this term with a playfulness that makes an ironic contrast with its historical meaning. A true story: One Bob Sjoberg, new at the MIT AI Lab, expressed some annoyance at the incessant use of jargon. Over his loud objections, GLS and RMS made a point of using as much of it as possible in his presence, and eventually it began to sink in. Finally, in one conversation, he used the word canonical in jargon-like fashion without thinking. Steele: “Aha! We've finally got you talking jargon too!” Stallman: “What did he say?” Steele: “Bob just used ‘canonical’ in the canonical way.”
Of course, canonicality depends on context, but it is implicitly defined as the way hackers normally expect things to be. Thus, a hacker may claim with a straight face that ‘according to religious law’ is not the canonical meaning of canonical.