[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 `kanon' (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'.